Answer
$y\sqrt[3]{2y}$
Work Step by Step
Extracting the factors that are perfect powers of the index of the radical, the given expression, $
\sqrt[3]{54y^4}-y\sqrt[3]{16y}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{27y^3\cdot2y}-y\sqrt[3]{8\cdot2y}
\\\\=
\sqrt[3]{(3y)^3\cdot2y}-y\sqrt[3]{(2)^3\cdot2y}
\\\\=
3y\sqrt[3]{2y}-y(2)\sqrt[3]{2y}
\\\\=
3y\sqrt[3]{2y}-2y\sqrt[3]{2y}
.\end{array}
By combining like terms, the expression above becomes
\begin{array}{l}\require{cancel}
(3y-2y)\sqrt[3]{2y}
\\\\=
y\sqrt[3]{2y}
.\end{array}