The Disappearing Act

Head to Nick Valentine's office in Diamond City and pick up the Earl Sterling Case File on the desk to start this quest.

First you have to access Earl Sterling's house for clues. You can pick the Novice lock on his door or get the key from Vadim Brobov in the Dugout Inn. Be careful of the first option however since if you're caught in the act, the city security will be hostile towards you.

Once you're inside, search for the Surgery Receipt on the floor beside the sofa. Leave the house then head to the Mega Surgery Center and talk to Dr. Sun. You can talk to him about the receipt by passing two speech checks. Once you bring up how to access the cellar, you'll have several options, like bribing, threatening, or convincing him. You can also attempt to pickpocket the key from Dr. Sun. Once you have the key, enter the cellar.

Confront Dr. Crocker and you'll have two speech options to arrest him or end peacefully. The other option is to kill him. If you selected the two other options, Dr. Crocker will commit suicide. Loot his body then Dr. Sun will come down and check up on you. After talking to him, you can leave the cellar and report back to Ellie to complete your quest and receive the reward.