Problem 142

When two standard six-sided dice are rolled, there are $6 \times 6 = 36$ possibilities for the
pair of numbers that are rolled.

Of these, the pairs $2 \times 6$,
$3\times 4$, $4\times 3$, and $6 \times 2$ each give $12$. (If one of the numbers rolled is
$1$ or $5$, the product cannot be $12$.)

Since there are $4$ pairs of possible
rolls whose product is $12$, the
probability that the product is $12$
is $\frac{4}{36}$.