1. The problem asks to find $f^{-1}(4)$, which means we want to find the value of $x$ such that $f(x) = 4$. 2. From the table, we look for the output value 4 in the row of $f(x)$ values: $-5, -2, 1, 3, 4$. 3. We see that $f(x) = 4$ when $x = 6$. 4. Therefore, $f^{-1}(4) = 6$. Final answer: $\boxed{6}$