#### Answer

$\dfrac{12}{5\sqrt{42}}$

#### Work Step by Step

Rationalizing the numerator, the given expression, $
\dfrac{2\sqrt{6}}{5\sqrt{7}}
,$ is equivalent to
\begin{array}{l}
\dfrac{2\sqrt{6}}{5\sqrt{7}}\cdot\dfrac{\sqrt{6}}{\sqrt{6}}
\\\\=
\dfrac{2\sqrt{6^2}}{5\sqrt{42}}
\\\\=
\dfrac{2(6)}{5\sqrt{42}}
\\\\=
\dfrac{12}{5\sqrt{42}}
.\end{array}