AMC 12 2002b Problem 16

Juan rolls a fair regular octahedral die marked with the numbers $1$ through $8$. Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3?

$\mathrm{(A)}\ \frac1{12} \mathrm{(B)}\ \frac 13 \mathrm{(C)}\ \frac 12 \mathrm{(D)}\ \frac 7{12} \mathrm{(E)}\ \frac 23$