Looking at the formula, you notice y = 0 when x = 0, or x = 2 or x = -2, so these are your x-intercepts. so draw these lines on your graph, where they cut the x-axis is where y=x(x-2)(x+2) will cut the x-axis. then plug in numbers in the different intervals.
you will have the interval (-inf, -2) and (-2, 0) and (0, 2) and (2, inf). when you plug in an x in each interval, you will get a positive or negative number. if the number is positive, the graph is above the x-axis in that interval, if the number is negative, the graph is below the x-axis in that interval. so for
(-inf, -2) plug in x = -3 for example, you get y = -15 < 0, the graph is below the x-axis
(-2, 0) plug in x = -1 for example, you get y = 3 > 0, the graph is above the x-axis
(0, 2) plug in x = 1 for example, you get y = -3 < 0, the graph is below the x-axis
(2, inf) plug in x = 3 for example, you get y = 15 > 0, the graph is above the x-axis
now hopefully you know what shape the graph will have, when expanded you will get an x^3 graph, so you will have two turns, and one end going to + infinity and the other going to -infinity
The graph is below. you should study all the transformation rules in your text book. texts books usually have the rules in one highlighted section