Answer
Th zeros are $x=3$ with multiplicity 1 and $x=-6$ with a multiplicity of 3. At $x=3$ and $x=-6$ the graph will cross the $x\text{-axis}$.
Work Step by Step
For zeros:
Let $f\left( x \right)=0.$
That is,
$\begin{align}
& 4\left( x-3 \right){{\left( x+6 \right)}^{3}}=0 \\
& \left( x-3 \right){{\left( x+6 \right)}^{3}}=0.
\end{align}$
Then the value of x is as follows:
$x=3,-6$
For multiplicity,
$x=3$, with a multiplicity of 1, because of $\left( x+5 \right)$.
$x=-6$, with a multiplicity of 3, because of $\left( x+5 \right)$.
Now,
The multiplicity of $x=3$ is odd; the graph will cross only the $x\text{-axis}$.
The multiplicity of $x=-6$ is odd; the graph will cross only the $x\text{-axis}$.
