Mogwin the artist asks you to find their missing masterpiece, to prove your trustworthiness.
This quest is available if you have completed the quest Mountaintop Diplomacy.
Starting the Quest
Talk to Mogwin in Moghome in the Churning Mists to begin the quest.
Question Moghome Inhabitants
Go south from Mogwin to the first quest icon on the map and talk to Mogomo.
Go south from Mogomo to the next quest icon on the map and talk to the Muddled Moogle.
Go east from there to the next quest icon on the map and talk to Mogtoe.
Speak with Mogwin
Go to the quest icon on the map and talk to Mogwin.
Obtain the Moogle Masterpiece
Go southeast from Mogwin until you are near Mogtoe (one of the three moogles you questioned). Go north up the slope near Mogtoe until you are outside. Go counter-clockwise along the edge of the rocks above Moghome to reach the orange circle on the map. Go to the west side of the circle and check on the sparkling Painted Stone.
Deliver the Moogle Masterpiece
You can either go clockwise around the edge of the rocks above Moghome to reach the slope that you came up, or you can just jump down below. Go to the quest icon on the map and talk to Mogwin to hand over the Moogle Masterpiece and complete the quest.