[tex]{( \sqrt[3]{{x}^{2}})}^{6} = {({x}^{ \frac{2}{3}})}^{6} = {x}^{ \frac{2}{3} \times 6 } = {x}^{2 \times 2} = {x}^{4} \\ [/tex]
So the answer is the second option which is,
[tex] {x}^{4} [/tex]
