She convinces him Penelope is about to marry Eurymachus.
Explanation:
In Book 15 of <em>The Odyssey</em>, we see that Athena travels to Sparta in order to find Telemachus. Athena tells him that Penelope is about to marry Eurymachus, and this convinces Telemachus of coming back to Ithaca. She also warns him of an ambush. The next day, Telemachus announces his departure and says goodbye to Helen and Menelaus.
