Answer
$\dfrac{-3\sqrt{6}-6}{2}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{-3}{\sqrt{6}-2}
$ results to
\begin{array}{l}
\dfrac{-3}{\sqrt{6}-2}
\cdot
\dfrac{\sqrt{6}+2}{\sqrt{6}+2}
\\\\=
\dfrac{-3\sqrt{6}-6}{(\sqrt{6})^2-(2)^2}
\\\\=
\dfrac{-3\sqrt{6}-6}{6-4}
\\\\=
\dfrac{-3\sqrt{6}-6}{2}
.\end{array}