The x intercepts of a parabola are (6,0) and (-2,0) determine the x coordinate of the vertex

This means that (x-6) (x+2) = f (x) is the equation for the parabola due to that if you plug these in, when x=6 and x=-2 then y=0. Expanding it, we get

x^2+2x-6x-12=x^2-4x-12. Since the x coordinate of the vertex is - b/2a, it's 4/2=2