Answer
$-4-2\sqrt{7}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{6}{2-\sqrt{7}}
$ results to
\begin{array}{l}
\dfrac{6}{2-\sqrt{7}}
\cdot
\dfrac{2+\sqrt{7}}{2+\sqrt{7}}
\\\\=
\dfrac{12+6\sqrt{7}}{(2)^2-(\sqrt{7})^2}
\\\\=
\dfrac{12+6\sqrt{7}}{4-7}
\\\\=
\dfrac{12+6\sqrt{7}}{-3}
\\\\=
-4-2\sqrt{7}
.\end{array}