Answer
$(x-2)\sqrt[3]{6x}$
Work Step by Step
Simplifying the radical terms by extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{6x^4}-\sqrt[3]{48x}
\\\\=
\sqrt[3]{x^3\cdot6x}-\sqrt[3]{8\cdot6x}
\\\\=
\sqrt[3]{(x)^3\cdot6x}-\sqrt[3]{(2)^3\cdot6x}
\\\\=
x\sqrt[3]{6x}-2\sqrt[3]{6x}
.\end{array}
Combining the like radicals results to
\begin{array}{l}\require{cancel}
x\sqrt[3]{6x}-2\sqrt[3]{6x}
\\\\=
(x-2)\sqrt[3]{6x}
.\end{array}
