that he was going to be assinated in Cuba? He was telling Fredo during the scene where he was having drinks together.

I don't think there's any specific answer to how Michael knew.

He had already figured out that Roth was behind the Tahoe attack, so from there it would stand to reason that Roth would knock Michael off in Cuba, which was Roth's territory and where Michael had very little security.

But as to how Michael would have known the specifics of Roth's assassination plans ("they're gonna take me home in a military car..."), I don't know. It's unlikely that Michael had a mole close to Roth, so I'll chalk that one up to directorial license.

I dont think it was that hard for mike to figured out. He already knew that roth tried to kill him at the beginning. I have always felt that roth was one of the more smarter and cunning characters in the Godfather films

I think that, since Michael knew Roth was behind the Tahoe attack, he knew that Roth wanted him in Havana--where Roth was the most powerful gringo--for one purpose: to have him killed. The plan to have him taken to his hotel in a military car, "for his own safety," was the dead giveaway (no pun intended).

An inviolate rule in all three pictures is that when anyone tells another character he is doing something for "his own safety" it means there's a plan to assassinate.

As Woltz has stated, how did Michael find out the details of his intended assassination? That means Michael had sources in Cuba. So, was Michael really walking into the lion's den?

Don't think so. He had his own plans. He told Fredo that Roth would never see the New Year, and we know what the body guard did to Johnny Ola. Michael was by no means improvising.

A miniscule point I've noticed after many years of rewatching; I've done several searches and didn't find anything, so excuse me if this has already been pointed out:

When Michael's out on the town in Havana and Fredo takes the group to the bar with "Superman", Michael glances over his left shoulder at his bodyguard a few rows behind him. When Fredo let's his secret slip about previously knowing Roth and Ola, Michael, before becoming too distraught from knowledge of Fredo's betrayal, turns to his right to look at his bodyguard. The bodyguard then immediately leaves to go murder Ola. So the pre-arranged signals were "a look from the left, everything's cool; a look from the right, go murder the people we talked about".

I'm not sure left or write had anything to do with it. It was probably the look on Michael's face that Buschetta interpreted as go.