If you spend enough time hanging out with the Railroad and doing quests for them, P.A.M. will eventually grant this quest. This assignment will take you to the Memory Den in Goodneighbor. Speak to Doctor Amari for the next step. Also, pick up the holotape on the table next to her and listen to it.
This quest is a straightforward Synth sweep at Malden Center. You can find this by heading north, following your waypoint indicator.
Simply take out all the Synths at the subway station. Be sure to look for an elevator to find the last batch of them.
Note: If you have already reached The Institution by this point and haven't alienated yourself from them, the Synths in this quest will not initially see you as a threat. This gives you an opportunity to get an upper hand by laying mines and firing away at them in advance.