To find the x-intercepts, or zeros, of the function, you'll need to solve (x-4) and (x+2) to separately, and make f(x) (aka the y) equal 0. From there you can solve.
[tex] x-4=0\\ x=4 [/tex]
[tex] x+2=0\\ x=-2 [/tex]
Using the (x,y) form, the x-intercepts are (4,0) and (-2,0).
In short, the second option, (-2,0), is the correct answer.
