These phrasal verbs in English are similar, but have different uses.
Find out means to discover information. Generally, we find out something by chance, in other words, we were not intentionally looking for the information.
Example: Jane found out her husband was cheating on her when she found the evidence in his jacket pocket.
Figure out means to learn some information by taking action to do it. Generally, we intend to figure out something. It does not happen by chance, as in find out.
Example: The police figured out how the robber was able to bypass the bank’s security.
So basically, you find out something by chance and you figure out something by your intention and effort.
This is based on my understanding. I hope other people can explain it as well.