Answer
$-8+4\sqrt{6}$
Work Step by Step
The given expression is
$=\frac{8}{\sqrt{6}+2}$
$=\frac{8}{2+\sqrt{6}}$
The conjugate of $2+\sqrt{6}$ is $2-\sqrt{6}$.
Multiply by $\frac{2-\sqrt{6}}{2-\sqrt{6}}$.
$=\frac{8}{2+\sqrt{6}}\cdot \frac{2-\sqrt{6}}{2-\sqrt{6}}$
Use product property of cube roots.
$=\frac{8(2-\sqrt{6})}{(2)^2-(\sqrt{6})^2}$
Simplify.
$=\frac{16-8\sqrt{6}}{4-6}$
$=\frac{16-8\sqrt{6}}{-2}$
$=-8+4\sqrt{6}$
