#### Answer

$2i+2i\sqrt{3}$

#### Work Step by Step

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $
\sqrt{-4}+\sqrt{-12}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{4}\cdot\sqrt{-1}+\sqrt{12}\cdot\sqrt{-1}
\\\\=
\sqrt{4}\cdot i+\sqrt{4\cdot3}\cdot i
\\\\=
\sqrt{(2)^2}\cdot i+\sqrt{(2)^2\cdot3}\cdot i
\\\\=
2i+2i\sqrt{3}
.\end{array}