#### Answer

$-3\sqrt{14}$

#### Work Step by Step

Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $
\sqrt{-6}\sqrt{-21}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{-1}\sqrt{6}\cdot\sqrt{-1}\sqrt{21}
\\\\=
i\sqrt{6}\cdot i\sqrt{21}
\\\\=
i(i)\sqrt{6(21)}
\\\\=
i^2\sqrt{(3\cdot2)(3\cdot7)}
\\\\=
i^2\sqrt{(3)^2\cdot14}
\\\\=
3i^2\sqrt{14}
\\\\=
3(-1)\sqrt{14}
\\\\=
-3\sqrt{14}
.\end{array}