Answer
$\dfrac{\sqrt{6xy}}{3y}$
Work Step by Step
Multiplying by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{2x}{3y}}
\\\\=
\sqrt{\dfrac{2x}{3y}\cdot\dfrac{3y}{3y}}
\\\\=
\sqrt{\dfrac{1}{(3y)^2}\cdot6xy}
\\\\=
\dfrac{1}{3y}\sqrt{6xy}
\\\\=
\dfrac{\sqrt{6xy}}{3y}
.\end{array}