Her mother asked her what would she do after she graduated from college.

The correct choice is "would." The sentence requires proper word order for indirect questions. In indirect questions, the subject typically precedes the verb, which differs from the structure of direct questions. In this case, "what would she do" is structured as a direct question, where "would" comes before the subject "she." However, since this is an indirect question following the mother’s inquiry, the correct construction should be "what she would do." Therefore, to maintain grammatical accuracy, the verb "would" should be changed to align with the indirect speech structure. This highlights the importance of adjusting the syntax when conveying indirect questions in English.