Answer
Continuous.
Work Step by Step
$f(x)$ will be continuous at $x=0$ if $f(0)=\lim_{x\to 0}f(x)$. We know that $f(0)=-1$.
$$\lim_{x\to 0}f(x)\\=\lim_{x\to 0}\frac{x^2-6x}{x^2+6x}\\=\lim_{x\to 0}\frac{x(x-6)}{x(x+6)}\\=\lim_{x\to 0}\frac{(x-6)}{(x+6)}\\=\frac{(0-6)}{(0+6)}=-1$$
$-1=-1$, hence it is continuous at $0$.