Why is this the answer?

One of the ways that you can check your work is to try turning the answer back into the original expression.

For choice B, raise the 2vw^2 to the power of 3.

(2vw^2)^3 = 8v^3w^6

When you move that back inside the cube root you get the cube root of 24v^3w^6, which is not the same as the original expression. You're still missing another w^2, which is why that appears in answer C.

Here's a video on simplifying roots that you may find helpful: https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-simplify-higher-index-roots/v/multiply-and-simplify-a-radical-expression-1

Thanks!