This is the 3106th most frequent Korean word.
가능해
"Possible" or "can be done."
In this sentence, '가능해' is used as an adjective phrase to describe the feasibility of the action of solving the problem.
그 방법으로 문제를 해결하는 것이 가능해.
Using that method, solving the problem is possible.
Here, '가능해요' is used in a question form to inquire about the possibility or feasibility of participating under specific circumstances.
제 상황에서 오늘 참여하는 게 가능해요?
In my situation, is it possible to participate today?
In the third example, '가능해' indicates the practicability or immediacy of carrying out a specific plan at the present moment.