Yes. Multiply out:
and find the coefficient of $x^9$. Do you see why this works?
EDIT: I'll elaborate more for the sake of completeness. It is because when you multiply:
Sorry for the yellow color, but treat each of these factors as one of the dice. Now to get a sum of $9$ on the dice, you are effectively picking powers of $x$ from each of the factors such that their exponents sum to $9$. The number of times you can pick powers of $x$ from each of the factors like that (which is the number of ways we can get a sum of $9$ on the dice) is exactly the coefficient of $x^9$ when the product is multiplied out.