Answer
$\color{blue}{\bf\text{false}}$
$\color{blue}{\bf(-2)\text{, not }2 \text{, is a zero with multiplicity }4}$
Work Step by Step
We are given the function $f(x)=(x+2)^4(x-3)$ and asked if
"$\text{2 is a zero with multiplicity 4}$" is true or false
We see that $(x+2)^4$ is raised to the power of $4$ and so it will have the same zero $4$ times.
However, the zero of $(x+2)$ is:
$x+2=0$
$x=-2$
So the statement is $\color{blue}{\bf\text{false}}$ because it is actually $(-2)$, not $2$ that is a zero with multiplicity 4
