Translation:I go to the library as often as possible.
I would say not "how possible" but "as possible" -- kiel can also mean "as, like" (li agas kiel reĝo "he acts like a king", etc.).
So this is actually not that far from the English "as often as possible" - literally, perhaps something like "as possible most often".
But it may be best to simply learn kiel eble plej X as a fixed template meaning "as X as possible" rather than analysing the individual words.
And you can't necessarily be expected to come up with that on your own - sometimes Duolingo courses teach you things by springing them on you and then showing you the right translation.