If you figure out a solution to a problem or the reason for something, you succeed in solving it or understanding it. ( INFORMAL )
It took them about one month to figure out how to start the equipment...
They’re trying to figure out the politics of this whole situation...
I don’t have to be a detective to figure that out.
= work out
PHRASAL VERB : V P wh / that , V P n (not pron) , V n P