Answer
$-2$
Work Step by Step
We first multiply the two quantities in the integrand, which result in the polynomial $8x^3 - 12x^2 + 2x - 3$
We now can take the integral of this polynomial, which is $2x^4 - 4x^3 + x^2 - 3x$
Now, we substitute the bounds of integration $2$ and $0$ and get the difference $(2(2)^4 - 4(2)^3 + 2^2 - 3(2)) - (0) = 32 - 32 + 4 - 6 = -2$