Answer
$\color{blue}{\bf{ 3x^4-9x^3-16x^2+12x+16 }}$
Work Step by Step
We are given the two functions $\bf{f}$ and $\bf{g}$
$\bf{f(x) = 3x^2 - 4 }$ and $\bf{g(x) = x^2 - 3x - 4 }$
We are asked to find $\bf{ ( f*g )(x) }$
$( f *g )(x) = (3x^2 - 4 )(x^2 - 3x - 4 ) $
$3x^4-9x^3-12x^2-4x^2+12x+16 $
$\color{blue}{\bf{ 3x^4-9x^3-16x^2+12x+16 }}$