If the number is divisible by 6, you know it must be divisible by 3.

We can show that the number is also divisible by 4.

If it is divisible by 4 and divisible by 3, it must be divisible by 12.

Case 1: is odd. Therefore .

So

.

So the number is divisible by 4.

Case 2: is even. Therefore .

So

.

So the number is divisible by 4.

Since the number is divisible by 3 and by 4, the number must be divisible by 12.