jmc

To solve for the $x$-intercept, we let $y$ equal 0, and then solve for the value of $x$ as shown: $$\begin{array}{rl}0-4& =4(x-8)\\ \Rightarrow -1& =(x-8)\\ \Rightarrow 7& =x\end{array}$$ Similarly, let $x$ equal 0, and solve for the $y$-intercept: $$\begin{array}{rl}y-4& =4(0-8)\\ \Rightarrow y-4& =-32\\ \Rightarrow y& =-28\end{array}$$ Therefore, the sum of the $x$ and $y$ intercepts is $7+(-28)=\boxed{-21}$.