A seemingly arbitrary flash “out of the blue,” through which the solution to a problem suddenly becomes apparent to you, but you do not consciously know how you “figured it out,” is called

Insight

Explanation:

Gaining solutions to problems may not always be straightforward, direct or contemporary reasoning. Solutions to some problems may take days, months, years or even decades. These sort of problems would usyaklybrequre team effort, togetherness, research to conquer. However, we sometimes make headway in getting problems solved through our subconscious system whereby lingering problems we have at heart suddenly becomes solvable. This kind of thinking whereby solutions to problems are attained is called insight which may stem as a result of several different knowledge sources which an individual has acquired, then Coming together to help unconsciously in solving difficult tasks.