Answer
$(3-x)\sqrt[3]{2x}$
Work Step by Step
Simplifying each term and then combining like terms, the given expression, $
\sqrt[3]{54x}-\sqrt[3]{2x^4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{27\cdot2x}-\sqrt[3]{x^3\cdot2x}
\\\\=
\sqrt[3]{(3)^3\cdot2x}-\sqrt[3]{(x)^3\cdot2x}
\\\\=
3\sqrt[3]{2x}-x\sqrt[3]{2x}
\\\\=
(3-x)\sqrt[3]{2x}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.