We have this possibility
f(x) = - (x+ 4)^2 (x - 0) ( x - 6) = -x^4 - 2 x^3 + 32 x^2 + 96 x
A zero of an odd multi[licity will cut through the x axis
A zero with an even multiplicity will just "kiss" the x axis
Since the graph goes to -infinity as x approaches both infinities, we need the " -" in front of the first term.......the end behavior of this term will overpower the end behavior of all the other terms
Heres a graph to get a feel for this :