You're reading it as the volume of revolution of the shaded area, yes? In that case there should be mention at least of the line x = 4.
Edit: sorry, I do agree with your 128/3 pi.
Your disc radius, i.e. the length of the strip in your pic, should be
and then the washer distance will be the same again. So you don't need to split it. Double is what you need to square before integrating with respect to y. Edit: no, pardon me. Doubling won't do. Didn't think it through. Sorry. More below.