Answer
$\dfrac{2\sqrt{2}}{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{4\sqrt{6}}{3\sqrt{12}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4}{3}\sqrt{\dfrac{6}{12}}
\\\\=
\dfrac{4}{3}\sqrt{\dfrac{\cancel{6}}{\cancel{6}(2)}}
\\\\=
\dfrac{4}{3}\sqrt{\dfrac{1}{2}}
\\\\=
\dfrac{4}{3}\sqrt{\dfrac{1}{2}\cdot\dfrac{2}{2}}
\\\\=
\dfrac{4}{3}\sqrt{\dfrac{2}{4}}
\\\\=
\dfrac{4}{3}\cdot\dfrac{\sqrt{2}}{\sqrt{4}}
\\\\=
\dfrac{4}{3}\cdot\dfrac{\sqrt{2}}{2}
\\\\=
\dfrac{2\cdot \cancel{2}}{3}\cdot\dfrac{\sqrt{2}}{\cancel{2}}
\\\\=
\dfrac{2\sqrt{2}}{3}
.\end{array}
