Answer
Domain: $x \ne \pm4$
Vertical asymptotes: $x=-4$
Horizontal asymptotes: $y=0$
Work Step by Step
Find the domain:
$x^2 -16 \ne 0$
$x^2\ne16$
$x \ne\pm 4$
Identify vertical asymptotes:
$\frac{x-4}{x^2-16}=\frac{x-4}{(x-4)(x+4)}=\frac{1}{x+4}$
$x=-4$
Identify horizontal asymptotes:
$f(x) \rightarrow$ as $x\rightarrow \infty$
$y=0$
