Note: This quest is available after completing the Institute main quest, Mankind Redefined. However, if you completed the Railroad quest Tradecraft , this quest will become unavailable even if you completed Mankind Redefined.
Talk to Justin Ayo of the SRB Division and he'll tell you to that someone within The Institute might be helping synths escape. He'll ask you to investigate Alan Binet of Robotics so head there. You don't have to question Binet directly; just head to Robotics and check the terminal logs there.
Once the quest is updated, head to the Binet quarters and read the terminal logs from there as well. Now head back to SRB and read the terminal logs there. The quest marker will Lead you to the maintenance room where you'll find find Eve. Upon confronting her, she'll threaten you with a gun. You have the option to kill her or convince her to stand down through a hard Charisma speech check.
Whatever the outcome of that confrontation with Eve, talk to Liam back in their room. From there, you'll have the option to either report Liam to Dr. Ayo or frame Dr. Ayo. The former will award you with 1,000 caps immediately and end the quest. Choosing to frame Dr. Ayo will require you to tinker with his private terminal. Upon completion, report back to Liam to receive his unique glasses as reward.