Let $\boxed{N}$ mean the number of whole number divisors of $N$.  For example, $\boxed{3}=2$ because 3 has two divisors, 1 and 3.  Find the value of
\[\boxed{\boxed{11}\times\boxed{20}}.\]
$\text{(A)}\ 6 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 24$
$\boxed{\boxed{11}\times\boxed{20}}$
$11$ has $2$ factors, and $20$ has $\{1, 2, 4, 5, 10, 20\}$ as factors, for a total of $6$ factors.  Plugging $\boxed{11} = 2$ and $\boxed {20}= 6$:
$\boxed{2 \times 6}$
$\boxed{12}$
$12$ has factors of $\{1, 2, 3, 4, 6, 12\}$, so $\boxed{12} = 6$, and the answer is $\boxed{A}$