Dancing Hands first appear as a sub-boss found on the 10th floor of Thebel Block in Tartarus, encountered in a group of three. This group can be easily dealt with using Orpheus' Bash skill or any other Personas acquired with Strike attacks.
They will later impede the progress of the party during the first Full Moon Operation as they attempt to reach the front of the train and the Arcana Priestess shadow. Afterward, they will appear in Arqa Block as regular enemies.
Dancing Hands are found in Halls 5 through 8 of the Steamy Bathhouse in the Midnight Channel. They will generally appear mixed in with other types of Shadows and will play a support role for them. After being defeated, Dancing Hands may drop the Thick Hide material. Selling 10 Thick Hides at Daidara will unlock the Hard Boots weapon for Chie in the shop's inventory.
Persona 4 Golden
Dancing Hands are found in Baths 5 through 8 of the Steamy Bathhouse within the Midnight Channel. They will appear with other shadows and use their skill to support them. If left alone on the field, they will escape. Upon defeat they may drop Smoky Quartz. Only 5 thick hides are necessary to unlock the hard boots in Persona 4 Golden.