Location: Wudang Sect
Prerequisite: Complete Traitor
Petitioner: Master Qingxu
Reward: +10 Affinity with Mowen

In order to trigger this side quest you first need to complete Traitor, a short main story quest. Once that's done and you need to begin accumulating Affiliation Points again, head into Sanqing Hall and speak to Master Qingxu. Yi will ask about Mowen, who has been largely AFK since Mount Windless. Leave Sanqing Hall to begin the side quest.

Qingxu mentioned Tancheng City, and that's where you need to go. Follow the roads south / southeast out of Wudang Sect and they will, after passing a waterfall, bring you to Tancheng City. Entering the city at this point will put you in the middle of a quest line involving the Beggars' Sect, so be prepared for those missions if you haven't already done them.

Head straight north through Tancheng City, towards the Beggars' Sect Headquarters, and you'll hit a cut scene with Mowen. This will raise Yi's Affinity with Mowen, generate a bit of suspicion as to what Mowen was doing in Tancheng City, and end the quest.