Why did Michael kill Carlos connie's husband in the godfather?
His name is Carlo Rizzi
The reason Michael ordered Pete to kill Carlo was that he at
first blamed Carlo, for the slaughter of Santino/Sonny.
Why?
Because that Carlo beat Connie up, Connie called Sonny and Sonny
raced towards his sisters appartment to hurt Carlo.
This was only the start.
When the Barzini, Greene and the other Dons were done four
Michael had a meeting with Carlo, at the Corleone Compound.
Here Michael tricks Carlo to say that he was supposed to trick
Sonny (As a favour for Don Barzini). Michael gives Carlo a ticket
to Las Vegas, but when Carlo is sitting in the car, Pete Clemenza
(the Capo) jumps up from behind and guillotines Carlo.