Answer
$\dfrac{4\sqrt{6}}{9}$
Work Step by Step
Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $
\dfrac{4\sqrt{2}}{3\sqrt{3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4\sqrt{2}}{3\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}
\\\\=
\dfrac{4\sqrt{6}}{3\cdot3}
\\\\=
\dfrac{4\sqrt{6}}{9}
.\end{array}