When a function has a zero with an even multiplicity, there is no sign shift for the function at that zero.
If the zero has odd multiplicity, the function shifts its sign at that point.
Since the function has zeros at -4, -1 and 2, those must be the points where the function touches the X-axis. Options A and C display this feature.
Nevertheless, the only even multiplicity is for the zero x=-1, so the function must have sign shifts at x=-4 and x=2, but no sign shift at x=-1. This is correctly displayed on option C.
Therefore, the graph that correctly represents the described function is that from option C.