First, the puzzle is: 2, 3, 4, 6. I need to use these numbers to make 24. This is a 24 game, where I have to combine the numbers with arithmetic operations to get 24.

The operations allowed are probably addition, subtraction, multiplication, division, and maybe parentheses to group operations. I need to use each number exactly once.

So, the numbers are 2, 3, 4, and 6. I need to form an expression that equals 24.

Let me think about factors. 24 can be factored in several ways, like 6 times 4, 8 times 3, 12 times 2, 24 times 1, etc. Since I have a 6 and a 4, maybe I can do 6 multiplied by 4, but that's only two numbers, and I have to use all four.

6 times 4 is 24, but I have to incorporate 2 and 3 as well. So I need to use all four numbers.

Perhaps I can do something like (6 × 4) × (something with 2 and 3), but 6×4 is 24, and I need to multiply by 1 or add 0 to keep it 24, but I have to use 2 and 3.

Maybe division or subtraction can help.

Another idea: 6 × 3 = 18, and 4 × 2 = 8, but 18 + 6 is 24, no, 18 + 6 is 24, but I used 6 twice? No, 6 is used once.

Let's list: if I do 6 × 3 = 18, then I have 4 and 2 left. 4 × 2 = 8, but 18 and 8, how to make 24? 18 + 6 is not possible, or 18 × something, but I need to combine.

Perhaps (6 × 3) + (4 × 2) / something, but that might not work.

(6 × 3) + (4 × 2) = 18 + 8 = 26, which is more than 24. Not good.

(6 × 4) × 1, but no 1, and I have 2 and 3.

Division: 6 / 2 = 3, but then I have 3 and 3 and 4, not helpful.

Another approach: 24 is 48 divided by 2, but 48 might be made from others.

Let me think about multiplication. Since 24 is a product of numbers.

For example, 8 × 3 = 24, and I have a 3, so if I can make 8 from 2,4,6.

How to make 8? 4 × 2 = 8, then 8 × 3 = 24, but I have a 6 left unused. I need to use all four numbers.

If I do 4 × 2 = 8, then I have 3 and 6, so (4 × 2) × 3, but that's 24, but missing the 6. Still, I need to include 6.

Perhaps (4 × 2) × 3 × (6/6) but that uses 6 twice, no, I have only one 6.

I need to incorporate the 6 in a way that doesn't change the value, like multiplying by 1 or adding 0.

For example, (4 × 2 × 3) × (6/6) but 4×2×3=24, and 6/6=1, so 24×1=24, but I'm using the 6 twice in (6/6), which is not allowed because I have only one 6.

In the expression, (6/6) uses the number 6 once for numerator and once for denominator, but in terms of the digits, I think it's using the number twice, which is not permitted. In 24 game, you have to use each card exactly once, so I can't use a number more than once.

So, I need an expression that uses each number once.

Perhaps division: like 6 / (1/4) or something, but I have to use 2 and 3.

Let's list all possible combinations.

I have four numbers: 2,3,4,6.

Operations: +, -, ×, ÷, and parentheses.

One common way is to use the numbers to make factors.

For instance, 6 and 4 can be multiplied to 24, but need to include 2 and 3.

(6 × 4) × (3 - 2) / 1 or something, but 3-2=1, so (6×4) × (3-2) = 24 × 1 = 24. That uses all four numbers: 6,4,3,2.

Let me write the expression: (6 × 4) × (3 - 2) = 24 × 1 = 24.

Is that allowed? Operations: multiplication and subtraction.

And it uses each number once.

I could write it as 6 × 4 × (3 - 2).

Yes, that should be fine.

But let me confirm: 3 - 2 = 1, then 6 × 4 = 24, 24 × 1 = 24. Perfect.

I could do division: for example, 6 ÷ (1/4) but I need to make 1/4 from 2 and 3, which might not work easily.

Another way: (6 - 2) × (4 + 3 - something), 6-2=4, 4+3=7, 4×7=28, not 24.

Not good.

Or (6 + 2) × (something), 8 × 3 = 24, but I have 4 left.

8 × 3 = 24, but 8 from 6+2, then 3 is used, but I have 4 unused.

Unless I do (6+2) × 3 × (4/4) but again, using 4 twice.

Not allowed.

Another idea: 4 × (6 ÷ 2) × 3, but 6÷2=3, then 4×3×3=36, which is 36, too big.

Not 24.

(4 × 6) ÷ (3 - 2) / something, 4×6=24, 3-2=1, 24 ÷ 1 =24, same as before.

In this case, (4 × 6) ÷ (3 - 2) = 24 ÷ 1 = 24.

Slightly different, but same thing.

(3 - 2) is 1, which is fine.

I could use division differently.

For example, 48 ÷ 2 = 24, and 48 can be 6 × 8, but no 8.

6 × 4 × 2 / 2, but again, using 2 twice.

Not good.

Perhaps with addition: 6 × 3 = 18, 4 × 2 = 8, 18 + 6 not possible.

(6 × 4) - 0, but no 0.

Another combination: 24 is 12 × 2, and 12 can be 3 × 4, so (3 × 4) × 2, but that's 24, but I have 6 unused. Same problem.

Unless I do (3 × 4 × 2) × (6/6) but again, invalid.

So the only way I see so far is to use subtraction to make 1, like (3-2)=1 or (6-4) or something.

With 6 and 4, 6-4=2, but I already have a 2, might be redundant.

For example, (6 - 4) = 2, but I have a 2, so I can do something like that, but need to incorporate.

Suppose I do (6 - 4) × something, (6-4)=2, then I have 2,3, and the other 2? No, (6-4) uses 6 and 4, produces 2, but I still have the original 2 and 3 to use.

So numbers left: original 2 and 3, plus the result 2, but in expression, it's messy.

Better to stick with the first idea.

Another expression: 6 × (4 - 2/2) or something.

2/2=1, 4-1=3, then 6×3=18, not 24.

Not good.

(6 × 4) / (2/3) or something.

2/3 is fraction, (6×4)/(2/3) = 24 / (2/3) = 24 × 3/2 = 72/2 = 36, not 24.

Not good.

Perhaps addition: 6 + 6 × 3, but no, 6+18=24, but only two numbers? 6 and 3, but 6×3=18, then +6, but I need another 6.

Not possible.

(4 + 2) × 3 = 6×3=18, not 24, and missing 6.

(4 + 2) × 4, but no extra 4.

I think the simplest is to use (3-2) or (4-3) or something to make 1.

With the numbers, since I have 2 and 3, (3-2)=1 is straightforward.

Similarly, (6/3)=2, but I have a 2 already.

For example, if I do (6/3) =2, then I have that 2, and original 2 and 4.

Then I can do (6/3) × 4 × 3, but (6/3)=2, then 2 × 4 × 3 = 24, but I used 3 twice? No: (6/3) uses 6 and 3, so in expression: (6 ÷ 3) × 4 × 2, but I have to use the original 2 as well.

Let's write: numbers used: 6,3 for (6÷3)=2, then I have original 2 and 4.

So expression: (6 ÷ 3) × 4 × 2 = 2 × 4 × 2 = 16, not 24. Because I have an extra 2.

(6 ÷ 3) × 4 × 2, that's three numbers, and I have four positions, but (6÷3) is one operation, using two numbers.

In terms of the expression, it uses three numbers: 6,3,4, and then ×2, so all four: (6 ÷ 3) × 4 × 2.

But (6÷3) is 2, 2 × 4 = 8, 8 × 2 = 16, not 24.

If I do (6 ÷ 3) × (4 × 2) × something, 4×2=8, 2×8=16, same.

Not 24.

(4 × 6) ÷ (3 ÷ 2) or something.

3 ÷ 2 = 1.5, (4×6)=24, 24 ÷ 1.5 = 16, not 24.

Not good.

Another idea: 24 = 6 × 4, and to incorporate 2 and 3, perhaps by division or subtraction.

I think (6 × 4) × (3 - 2) is fine.

Similarly, I could do (3 × 8) but no 8.

(4 × 3) × 2 = 24, missing 6.

Unless I do (4 × 3 × 2) × (6/6) but invalid.

Perhaps exponentiation, but I think in standard 24 game, only basic operations are used, no exponents.

So, I think subtraction or division to make 1 is acceptable.

Another common way: (6 - 2) × (4 + 1) but no 1.

4 + 1 not available.

(6 + 2) × 3 = 8×3=24, missing 4.

But if I can make it with 4 in a cancelling way.

For example, (6 + 2) × 3 × (4/4) but again, using 4 twice.

Not allowed.

Perhaps (6 × 3 - 2) × 2 or something, 18-2=16, 16×2=32, not 24.

Not good.

So, back to the first solution.

Perhaps division: 48 ÷ 2 = 24, 48 from 6 × 8, but no 8.

6 × 4 = 24, same as before.

I think I should go with (6 × 4) × (3 - 2) = 24.

To write it in a single expression: 6 × 4 × (3 - 2)

Or with operations: multiplication and subtraction.

Another expression: 6 × (4 × 3 - 12) but no 12.

Not helpful.

(4 - 2/2) × 6, 2/2=1, 4-1=3, 3×6=18, not 24.

No.

I think it's fine.

Perhaps using the numbers in a different order.

For example, 3 × (8) but no 8.

2 × (12) and 12 from 4 × 3, but missing 6.

Same issue.

So, I believe the intended solution is to use (3-2) to make 1.

Therefore, one possible solution is: (6 × 4) × (3 - 2) = 24

To write it without parentheses, but it might need parentheses for order.

6 × 4 × (3 - 2) is clear.

Another way: 6 × 4 ÷ (3 - 2) × (3 - 2) no.

(6 × 4) ÷ (3 - 2) but 3-2=1, division by 1, same as multiplication.

(6 × 4) ÷ (3 - 2) = 24 ÷ 1 = 24.

But subtraction is fine.

In terms of points, it should be acceptable.

Perhaps there's another combination.

What about (6 / 2) × (4 × 3) / 2 or something, 6/2=3, 4×3=12, 3×12=36, not 24.

No.

(6 × 3) ÷ (2/4) or something, 2/4=0.5, 18 ÷ 0.5 = 36, not 24.

Not good.

I think I should conclude.

So for the numbers 2,3,4,6, one solution is 6 × 4 × (3 - 2) = 24

To present it nicely.