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 \[\boxed{\boxed{11}\times\boxed{20}}\]
Both $1$ and $11$ divide $11,$ so $11}=2$, and since $1,$ $2,$ $4,$ $5,$ $10,$ and $20$ divide $20,$ then $\boxed{20}=6$. The inner expression, $\boxed{11}\times\boxed{20}=2\times6=12$. Finally, $\boxed{12=6$ because $1,$ $2,$ $3,$ $4,$ $6,$ and $12$ divide $12.$

Therefore, $6$ is our answer. Please note that we have not boxed the correct answer as we normally do, as that would be especially confusing for this problem.