Answer
$-\dfrac{17\sqrt{6}}{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{\dfrac{2}{3}}-2\sqrt{54}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{2}{3}\cdot\dfrac{3}{3}}-2\sqrt{9\cdot6}
\\\\=
\sqrt{\dfrac{6}{9}}-2\sqrt{(3)^2\cdot6}
\\\\=
\dfrac{\sqrt{6}}{\sqrt{9}}-2\cdot3\sqrt{6}
\\\\=
\dfrac{\sqrt{6}}{\sqrt{(3)^2}}-6\sqrt{6}
\\\\=
\dfrac{\sqrt{6}}{3}-6\sqrt{6}
\\\\=
\dfrac{\sqrt{6}}{3}-\dfrac{18}{3}\sqrt{6}
\\\\=
-\dfrac{17\sqrt{6}}{3}
.\end{array}
