Answer
$f(x)=x^3/3 - (4 x)/3$
Work Step by Step
If $a$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “multiplier” of the function.
Hence here $f(x)=kx(x+2)(x-2)$
$(-4,16)$ is on the graph thus $k\cdot(-4)(-2)(-6)=16\\48k=16\\k=\frac{1}{3}$
So $f(x)=\frac{1}{3}x(x+2)(x-2)=x^3/3 - (4 x)/3$
