Danish "muligt" and Dutch "mogelijk" are cognates, both meaning "possible".
Danish "muligt" is from Middle Low German (middelnedertysk) "mogelik".
And both are related to the English words "may" and "might" (is permitted; is possible; has the power to do something). See also German Macht, and (I believe) Danish magt.
"Possible" on the other hand is in English from Latin via French and replaced the Old English "mihtlic". "ġyf ðū ġelȳfan mǣġe, ealle þing synd ġelȳfedum mihtlīċe" (If you have the power to believe, all things are to the believer possible).