To multiply polynomials, take every term from one polynomial and multiply it by every term in the other, so a simple example:
(a + b)(x + y) = ax + ay + bx + by
you can see that a was multiplied by both terms (x and y) as was b, then the results are all added together.
So your problem:
(4x³ + 8x)(x² - 1)
same thing, just being sure to keep track of exponents. 4x³ gets multiplied by both terms in the other, as does 8x, to give:
4x⁵ - 4x³ + 8x³ - 8x
Now we can combine like terms to simplify:
4x⁵ + 4x³ - 8x
Option D is your answer.