infer vs figure out

infer and figure out both are verbs.

Word	Noun	Adjective	Verb	Adverb
infer	No	No	Yes	No
figure out	No	No	Yes	No

As verbs, figure out is a hypernym of infer; that is, figure out is a word with a broader meaning than infer:

infer: guess correctly; solve by guessing
figure out: find the solution to (a problem or question) or understand the meaning of

Other hypernyms of infer include lick, puzzle out, solve, work, work out.

infer (verb)	figure out (verb)
reason by deduction; establish by deduction	find the solution to (a problem or question) or understand the meaning of
believe to be the case
guess correctly; solve by guessing
conclude by reasoning; in logic
draw from specific cases for more general cases