Ways for eight dice to total twelve

Eight fair six-sided dice are rolled. Writing the probability that their faces add up to $12$ as $\dfrac{x}{6^8}$, find $x$.

330. Every die shows at least $1$, accounting for $8$; the other $4$ pips are spread over $8$ dice, and no die can exceed $6$. By stars and bars that is $\binom{4+8-1}{4}=\binom{11}{4}=330$ outcomes.