### Instruction: 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?### Response: 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.