I don't know if he killed 8 Made guys, but him and Nardi were responsible for a couple of Cleveland guys being blown up, and they were also supposedly involved in the disappearance of Lips Moceri. And yeah, Nardi had ambitions of becoming boss of the Cleveland Family, I think Greene was aware of this as well, felt like if Nardi was at the top, he wouldn't have to take orders anymore or give the Italians a cut of whatever he was doing, I suppose.