We want to find the x-intercepts of the polynomial

this means, we want to find where this functon crosses the x axis. Recall that the x axis is the line y=0. So we want to solve this equation

if we multiply both sides by -1, we get

on the right, we have a difference of squares, so we can factor it out as

now, as this is a product of numbers, this means that each of the number could be 0. This means we have two different equations, which are

and

on the first one, if we subtract 4 on both sides, we get

and on the second one, if we add 4 on both sides, we get

so the x-intercepts of the polynomial are x=4 and x= -4