unmöglich
impossible
Describes something that cannot happen, exist, or be done; not feasible.
Es ist unmöglich, ohne Sauerstoff zu atmen.
It is impossible to breathe without oxygen.

impossible
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impossible
Describes something that cannot happen, exist, or be done; not feasible.
Es ist unmöglich, ohne Sauerstoff zu atmen.
It is impossible to breathe without oxygen.

The word is the direct opposite of 'möglich' (possible). The prefix 'un-' is often used in German to negate the meaning of adjectives.
Ohne das richtige Werkzeug ist die Reparatur unmöglich.
Without the right tool, the repair is impossible.
In the meaning of 'not feasible', 'unmöglich' (impossible) is very often used in the structure 'es ist unmöglich, etwas zu tun' (it is impossible to do something). This is followed by an infinitive clause with 'zu'.
Es ist unmöglich, diese Aufgabe in nur einer Stunde zu erledigen.
It is impossible to complete this task in just one hour.
If you want to describe behavior as unacceptable, you can say 'jemand benimmt sich unmöglich' (someone behaves unacceptably) or 'jemandes Verhalten ist unmöglich' (someone's behavior is unacceptable). This use expresses strong criticism.
Er hat sich auf der Feier allen Gästen gegenüber unmöglich benommen.
He behaved unacceptably toward all the guests at the party.
The use as an intensifier meaning 'extremely' is purely colloquial. In this function, 'unmöglich' (impossibly/extremely) stands directly before the adjective it intensifies.
Die Party gestern war unmöglich lustig.
The party yesterday was impossibly funny.
possible
'möglich' and 'unmöglich' are direct opposites when it comes to whether something can happen or be done. 'möglich' means: It can work, it is feasible, or it is conceivable. 'unmöglich' means: It cannot work or is not feasible. 'möglich' can also express that something may be true, but is not certain. 'unmöglich' rules out this possibility.

Wegen des starken Schnees war die Fahrt zum Dorf unmöglich.
Because of the heavy snow, the trip to the village was impossible.
Ein Termin am nächsten Tag war für das Team möglich.
An appointment the next day was possible for the team.