To find out = you discover or learn something. To figure out = you solve or work out/conclude something in your mind/reasoning. if your friend told you something about another friend of yours you have "found out" from/by a conversation/gossip from your friend. if you discover lipstick on the pillow of your partner that does not usually wear lipstick, you will probably figure out something strange is going on. if you saw a television documentary you would have found out something about the subject of the documentary if you have to search and enquire to learn the same information that you learnt from the documentary you will have "figured out" what you "found out" by watching the documentary. if you find some information about somebody or something by accident you will have found out about it/that if you have to use your brain and reasoning to learn something about anything or anybody you will have "figured it out" the clue is in the two phrases "to find" out and "to figure" to work figure it out yourself.

Hey! These phrasal verbs are similar, but their uses in certain circumstances slightly differ. For example, you would use 'figure out' when you have solved a problem or come to a realisation. This could be by yourself or someone else has helped you do that work. Some examples: I figured out the answer to the math homework. We figured out why he doesn't like me. Figured out implies that some work has been done to solve that problem or come to that realisation. For 'find out,' it doesn't imply that any work has been done by the subject. If I said, 'I found out the answer to the math homework', it doesn't imply that I have done any work to get the answer, the teacher or someone else could have just told me the answer. So, you would use 'find out' if you have gained knowledge of something without solving the problem yourself, normally you have been told something. Some examples: he found out that his dog died. Sarah will find out tomorrow that she didn't do well in her exam. I hope this makes sense and helps you!!