Answer
$\dfrac{\sqrt[3]{2}}{6}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\sqrt[3]{\dfrac{16}{27}}-\dfrac{\sqrt[3]{54}}{6}
\\\\=
\sqrt[3]{\dfrac{8}{27}\cdot2}-\dfrac{\sqrt[3]{27\cdot2}}{6}
\\\\=
\dfrac{2\sqrt[3]{2}}{3}-\dfrac{3\sqrt[3]{2}}{6}
\\\\=
\dfrac{2(2\sqrt[3]{2})-3\sqrt[3]{2}}{6}
\\\\=
\dfrac{4\sqrt[3]{2}-3\sqrt[3]{2}}{6}
\\\\=
\dfrac{\sqrt[3]{2}}{6}
.\end{array}
