Answer
$f(x)=x^4-15x^2+10x+24$
Work Step by Step
If $c$ is a zero of a function with multiplicity $b$ then $(x-c)^b$ is a “factor” of the function.
We are given that the degree is $4$, and the zeros are $-4$, $-1$, $2$ and $3$, hence
$f(x)=a(x+4)(x+1)(x-2)(x-3)\\
f(x)=a(x^4-15x^2+10x+24)$
If $a=1$, the function is
$f(x)=x^4-15x^2+10x+24$