#### Answer

$2\sqrt[3]{2wv^2}$

#### Work Step by Step

Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{4w}\sqrt{4v^2}
\\\\=
\sqrt[3]{4w(4v^2)}
\\\\=
\sqrt[3]{16wv^2}
.\end{array}
Extracting the factors that are perfect powers of the index, the expression above simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{16wv^2}
\\\\=
\sqrt[3]{8\cdot2wv^2}
\\\\=
\sqrt[3]{(2)^3\cdot2wv^2}
\\\\=
2\sqrt[3]{2wv^2}
.\end{array}