Answer
$4\sqrt{6}+4\sqrt{10}$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
4\sqrt{2}(\sqrt{3}+\sqrt{5})
,$ is equivalent to
\begin{array}{l}\require{cancel}
4\sqrt{2(3)}+4\sqrt{2(5)}
\\\\=
4\sqrt{6}+4\sqrt{10}
.\end{array}