Find out means to discover information(usually by chance). -I found out that my uncle used to be in the military. -She found out that her husband had cheated on her. -After they purchased the house, they found out that several murders had been committed in one of the bedrooms. Figure out means to learn some information by taking action to do it. -I can't figure out how to do this puzzle. I've been trying to figure it out for days. -If you figure out the answer to that question, let me know. I've been trying to solve it, but I just can't. -The police figured out who robbed the bank after they looked at the surveillance tape.

Find out is more like when you discover something, and figure out is used for a new information learned, with some effort put into it, when you needed to think, analyse the situation. I hope it helped :)