Answer
$f(x)=-2(x+4)(x+1)(x-2)$
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 $f(x)=k(x+4)(x+1)(x-2)$
$(0,16)$ (because of the y-intercept) is on the graph thus $k\cdot(4)(1)(-2)=16\\-8k=36\\k=-2$
So $f(x)=-2(x+4)(x+1)(x-2)$
