Would not - is correct as well. It implies you ask her in the past and she didn’t tell you in the past. Won’t is correct. It implies that in the present moment she is still not telling you what happened.

This exercise has two correct answers depending on context. Example 1 wouldn’t with the meaning « refused to do » Yesterday was very cold. I tried to take my dog for a walk, but he wouldn’t go. [= refused] See unit 47 of your book for verb changes for reported speech (the same verb changes apply for a description of a past situation and actions which occur before, during, or after the « present moment » in the description. Example 2 Won’t with the meaning « refused and will refuse the next time also » Yesterday, I asked my son why he quit the soccer team, but he won’t tell me. [= he wouldn’t tell me yesterday and he probably won’t tell me tomorrow] See unit 48 of your book for the choice of not putting verbs in the past when a situation that occurred in the past is still true now.