Which of the following is divisible by 6 when n is any integer?

A. (2n+3)(3n+2)
B. n(n+1)(n+2)
C. (2n+3)(3n-2)
D. n(n+2)(3n+6)

just expand each product, and see whether all the terms are divisible by 6.

For example,
(2n+3)(3n+2) = 6n^2+13n+6
You can see that 13n is not necessarily divisible by 6.

If you expand the others, you will see that one of them has all its terms multiples of 6.