Hello , Find out: -to determine, ascertain or establish after studying , surveying or experimenting . Also in the sense of discovering. - Get to know or become aware of usually by accident something that already exists as 李汉伦 mentioned before . - to detect wrongdoing . Figure out : work out , solve or understand. It has more to do with problem solving ,more related to issues where solutions has to be found

Find out = realise (somehow), some one else told you (发现， 得知 。。。) Figure out = you worked it out by yourself (算出， 弄明白 。。。)