Answer
$-8\sqrt[3]{4}$
Work Step by Step
Using the properties of radicals, the given expression, $
-2\sqrt[3]{108}-\sqrt[3]{32}
,$ simplifies to
\begin{array}{l}\require{cancel}
-2\sqrt[3]{27\cdot4}-\sqrt[3]{8\cdot4}
\\\\=
-2\sqrt[3]{(3)^3\cdot4}-\sqrt[3]{(2)^3\cdot4}
\\\\=
-2\cdot3\sqrt[3]{4}-2\sqrt[3]{4}
\\\\=
-6\sqrt[3]{4}-2\sqrt[3]{4}
\\\\=
-8\sqrt[3]{4}
.\end{array}