Анна исчезла из дверей так быстро, как могла, как только увидела его там.

English Translation

Anne got out the door as quickly as she could when she saw him there.

why is door (дверей) plural?

I asked a native Russian speaker. He says that из дверей might be a fixed expression. He goes on to say that in older buildings, there was often a pair of doors/gates, and you had to open both to get in or out. So it would make sense to treat doors as plural.