Suppose $f(x) = -x^2 + 6$. Evaluate the limit below by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).
$\displaystyle{\lim_{h \to 0} \Bigg( \frac{f(4+h)-f(4)}{h} \Bigg) = \lim_{h \to 0} \Bigg(}$ $\displaystyle{\Bigg) = }$ .