Answer
-3
Work Step by Step
$\frac{\sqrt -12\times\sqrt -6}{\sqrt 8}=\frac{i\sqrt 12\times i\sqrt 6}{\sqrt 8}=\frac{i^{2}\times\sqrt 12\times\sqrt 6}{\sqrt 8}=\frac{-1\times\sqrt (12\times 6)}{\sqrt 8}=\frac{-1\times\sqrt 72}{\sqrt 8}=-\sqrt\frac{72}{8}=-\sqrt9=-3$
We know that $\sqrt -1=i$, because $i^{2}=-1$.