Talk to Erin in Vault 81 to start this quest and agree to help her find her cat. Ashes is found outside the Vault, around the Chestnut Hillcock Reservoir area. Just follow the marker and it will lead you to her location near the shore to the NE. After finding Ashes, talk to it to send it home. Now return to Erin and talk to her to complete the quest. Completing this quest will also unlock the next quest, "Hole in the Wall".