#### Answer

$4\sqrt[]{6}-8\sqrt[]{15}$

#### Work Step by Step

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $
4\sqrt[]{3}(\sqrt[]{2}-2\sqrt[]{5})
,$ simplifies to
\begin{array}{l}\require{cancel}
4\sqrt[]{3}(\sqrt[]{2})-4\sqrt[]{3}(2\sqrt[]{5})
\\\\=
4\sqrt[]{6}-8\sqrt[]{15}
.\end{array}