Answer
$-2x \sqrt[3]{x}$
Work Step by Step
Factor the radicand so that some of the factors are perfect cubes:
$\sqrt[3]{-8x^4}\\
=\sqrt[3]{(-8x^3)\cdot x}\\
=\sqrt[3]{(-2)^3x^3\cdot x}$
Use $-2^3x^3=(-2x)^3$.
$=\sqrt[3]{(-2x)^3\cdot x}$
Use the rule $\sqrt[3]{ab}=\sqrt[3]{a}\cdot \sqrt[3]{b}$ to obtain:
$=\sqrt[3]{(-2x)^3}\cdot \sqrt[3]{x}$
Simplify.
$=-2x\sqrt[3]{x}$
Hence, the correct answer is $-2x \sqrt[3]{x}$.
