Question 821326
Read the zeros directly from the function definition and use them as critical points which define intervals along the x-axis.  

The zeros are at -2, 2, and 4.  You want to check a value for sign in each of the intervals:
{{{x<-2}}};
{{{-2<x<2}}};
{{{2<x<4}}};
{{{4<x}}}.


Intuitively, you would well guess that f(x) will be positive in {{{x<-2}}} and in {{{4<x}}}.


Try 0 within {{{-2<x<2}}}:
{{{(0-4)(0+2)^2(0-2)=(-4)(4)(-2)>0}}}, so positive.


Try 3 within {{{4<x}}}:
{{{(3-4)(3+2)^2(3-2)=(-1)(25)(1)<0}}}, negative.


You should sketch a graph based on these and you then can find where f touches or crosses the x-axis.  Note what happens around {{{x=-2}}}; positive on both sides near this, so f not cross the x-axis, but TOUCHES it only.


{{{graph(300,300,-5,5,-25,30,(x-4)(x+2)^2(x-2))}}}