Determine the value for $c$ so that $\underset{x4}{lim}f(x)$ exists.

$f(x)=\{\begin{array}{ccc}{x}^2-8,& \text{f}\text{o}\text{r}& x<mn\; id="EditorElement\_812545">4</mn>\\ -x^2+c,& \text{f}\text{o}\text{r}& x>4\end{array}$

The value of $c$ is