A line is described by the equation $y-4=4(x-8)$. What is the sum of its $x$-intercept and $y$-intercept?
To solve for the $x$-intercept, we let $y$ equal 0, and then solve for the value of $x$ as shown: \begin{align*}
0-4&=4(x-8)\\
\Rightarrow\qquad -1&=(x-8)\\
\Rightarrow\qquad 7&=x
\end{align*} Similarly, let $x$ equal 0, and solve for the $y$-intercept: \begin{align*}
y-4&=4(0-8)\\
\Rightarrow\qquad y-4&=-32\\
\Rightarrow\qquad y&=-28
\end{align*} Therefore, the sum of the $x$ and $y$ intercepts is $7+(-28)=\boxed{-21}$.