Answer
$6+4i\sqrt{6}$
Work Step by Step
Using $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ the given expression, $
2\sqrt{-24}+6
,$ is equivalent to
\begin{align*}
&
2\sqrt{-1}\cdot\sqrt{4}\cdot\sqrt{6}+6
\\&=
2\sqrt{-1}\cdot2\cdot\sqrt{6}+6
\\&=
2i\cdot2\cdot\sqrt{6}+6
&\text{ (use $i=\sqrt{-1}$)}
\\&=
4i\sqrt{6}+6
\\&=
6+4i\sqrt{6}
.\end{align*}
Hence, the given expression simplifies to $
6+4i\sqrt{6}
$.