The correct option is A finished
Adverbs modify verbs, adjectives and sometimes other adverbs in a sentence.
In this sentence, the adverb 'almost' modifies the verb 'finished'. It hints at time states that she is about to finish her work. So, Option A is correct.
Option B is incorrect as 'work' is a noun. Adverbs don't modify nouns.
Option C is incorrect as 'she' is a pronoun. Adverbs don't modify pronouns.
Option D is incorrect as 'her' is a possessive adjective which is not being modified by the adverb in this sentence.