jmc

There are $6\times 6=36$ possible outcomes. The only way that they can roll an odd product is if both their rolls are odd. Since 3 of the 6 faces on each die are odd, this can occur in $3\times 3=9$ ways. So a even product can occur in $36-9=27$ ways, and the probability is thus $\frac{27}{36}=\boxed{\frac{3}{4}}$.