How do you find the domain of (x^2-x-12)^-4?

${\left({x}^{2} - x - 12\right)}^{-} 4$ can be written as $\frac{1}{{x}^{2} - x - 12} ^ 4$
This will be undefined if $\left({x}^{2} - x - 12\right) = 0$, but defined for all other values of $x$ in $\mathbb{R}$.
${x}^{2} - x - 12 = \left(x - 4\right) \left(x + 3\right)$ is zero when $x = 4$ or $x = - 3$, so these are the only prohibited values of $x$ and the domain of the function is:
$\mathbb{R} \setminus \setminus \left\{- 3 , 4\right\}$
that is $\left\{x \in \mathbb{R} : x \ne - 3 \wedge x \ne 4\right\}$