Allie and Betty play a game where they take turns rolling a standard die. If a player rolls $n$, she is awarded $f(n)$ points, where  \[f(n) = \left\{
\begin{array}{cl} 6 & \text{ if }n\text{ is a multiple of 2 and 3}, \\
2 & \text{ if }n\text{ is only a multiple of 2}, \\
0 & \text{ if }n\text{ is not a multiple of 2}.
\end{array}
\right.\]Allie rolls the die four times and gets a 5, 4, 1, and 2. Betty rolls and gets 6, 3, 3, and 2. What is the product of Allie's total points and Betty's total points?
To find the product of Allie's and Betty's total points, I need to first find each of their total points by adding up the points they got from each roll. For Allie, she got a 5, 4, 1, and 2, which means she got 0, 2, 0, and 2 points respectively, according to the function f. So Allie's total points are 0 + 2 + 0 + 2 = 4. For Betty, she got a 6, 3, 3, and 2, which means she got 6, 0, 0, and 2 points respectively, according to the function f. So Betty's total points are 6 + 0 + 0 + 2 = 8. Now to find the product of Allie's and Betty's total points, I just multiply 4 and 8, which gives me 32. 