When rolling a red die and a green die, how many combinations of rolls will add to 6?

You can use the following generating function to find the number of ways two die will sum to 6.

\left(\sum_{k=1}^{6}x^{k}\right)^{2}

Expand and look at the coefficient of x^6. That's your answer.

Actually, it'd probably be easier for you to just write them out. There aren't that many.

G-1, B-5
G-2, B-4
B-1, G-5
G-4, B-2
B-3, G-3

That's about it.

The aforementioned generating function works nice if the sum needed is large, such as how many ways can 5 dice sum to 24? Now, that's a 'whole nuther' matter. However, if you used it you would see the 5x^6.