Hi belena, and welcome to Using English.
If you say "I wouldn't put it past him" it means you have suspicions about the person's honesty and ethics.
You and this person are working together on a project. You will not be there they day the project must be presented to your boss/teacher. You say to a friend "I'm afraid he will take all the credit for this and not let them know that I was part of this." Your friend says "I wouldn't put it past him."
A man ("Pete") is having some trouble with his girlfriend, although they both want to figure out how to solve their problems. In the meantime, "Joe" (another person) has always liked the girlfriend. Pete says to a friend "Joe will probably try to sleep with her while we are going through this." His friend says about Joe "I wouldn't put it past him. He tried to get her to go to bed with him when you guys first started dating."