Answer
$\lim\limits_{x \to 4} f(x) = f(4) = 8$
Work Step by Step
$f(x) = x + 4$, which is continuous for all real numbers $x$.
This means that the $\lim\limits_{x \to a} f(x) = f(a)$
So, to find the limit as $x$ approaches $4$, just plug $4$ into the function.
$\lim\limits_{x\to 4} x + 4 = (4) + 4 = 8$