She was fined . . . . . . . . parking her car . . . . . . . . no-parking area.

Preposition of reason indicates some relationship of a noun or pronoun with regard to some reason, cause or purpose. These prepositions include to, for, with the view to, in order to, so as to, because of, due to, for the purpose of, etc. The first blank will take 'for' preposition.
'No-parking area' is a place or location, so the preposition 'in' will be used in the second blank.