Answer
-2
Work Step by Step
$\frac{\sqrt -6\times\sqrt -2}{\sqrt 3}=\frac{i\sqrt 6\times i\sqrt 2}{\sqrt 3}=\frac{i^{2}\times\sqrt 6\times\sqrt 2}{\sqrt 3}=\frac{-1\times\sqrt (6\times 2)}{\sqrt 3}=\frac{-1\times\sqrt 12}{\sqrt 3}=-\sqrt\frac{12}{3}=-\sqrt4=-2$
We know that $\sqrt-1 =i$, because $i^{2}=-1$.