After returning to Father over bring Gabriel back in, he will mention that X6-88 spoke very highly of the Sole Survivor's skills, and will request for them to aid in the retrieval of a rather large group of synths that had recently escaped from the Institute, and are being protected by The Railroad over at the caravan town of Bunker Hill.
While there are many ways to complete this quest, only one method will result in no consequences from any of the major factions involved. If the player does not inform either the Railroad or the Brotherhood, they can simply enter Bunker Hill and retrieve the synths (relatively) unmolested.
Depending on how the player wants to progress this quest in the name of the Institute, they may either meet up with a courser in the alleys near Bunker Hill and keep close to him, which will require fighting through both the BoS and The Railroad attackers/defenders, or the courser can be left behind, in which the only true resistance the player will encounter, are the turrets set up by The Railroad, which will not turn the faction hostile when destroyed. All BoS attackers, and all Railroad defenders, will remain docile towards the player , allowing for them to reach the synths relatively unharmed.
Regardless of how the player approaches Bunker Hill, The BoS and Railroad will continue massacring each other, allowing the courser to catch up and teleport back to the Institute with the synths after finding their hiding place, and speaking their code phrases.
So long as the player does not kill any of the attackers or the defenders, with the sole exception of The Railroad turrets, no negative consequences will happen with the other major factions.
The Railroad method:
The Railroad will ask for the player to free the trapped synths, requiring for them to fight through the BoS and Institute invaders.
After clearing the way and then freeing the synths, they will run off to an unknown extraction point. This may lead to banishment from the Institute if the player openly states that they released the synths in the subsequent meeting with Shaun.
The Brotherhood of Steel method:
The Brotherhood of Steel will ask for the player to kill the trapped synths, in a clear message of open hostility towards the Institute. In order to kill the synths, the player will be forced to deal with both the Institute and The Railroad.
After dealing with the synths, the Railroad and the Institute will chew the player out, but as long as they don't openly admit to killing them for the Brotherhood, they can remain on friendly terms.
Regardless of what method the Sole Survivor chooses, they will need to fight their way through the C.I.T. ruins, which have been largely taken over by super mutants, who are entrenched within fighting waves of Institute generation 1 synths. After reaching the roof of the ruins, Father will be found looking over the Boston ruins, and pondering its future. After explaining the Sole Survivor's actions at Bunker Hill, Father will teleport back to the Institute, and must be followed shortly after.
Brotherhood of Steel
Speak to Father
I need to find out what Shaun wants.
Reach Bunker Hill
I've been tasked with helping to recover synths that have escaped from the Institute and fled to Bunker Hill. There's a courser waiting for me just outside the settlement.
(Optional) Inform the Brotherhood
(Optional) Inform the Railroad
Find the Escaped Synths
Working with a Courser from the Institute, I need to find the escaped synths hiding in Bunker Hill. I've warned the Brotherhood, who wants the synths destroyed.
Deal With the Escaped Synths
We've found the escaped synths. Now to either issue their recall codes, or destroy them.
Kill the Courser
Speak with Father in the ruins of CIT.
I need to return to the Institute and tell Shaun what happened in Bunker Hill.
Regardless of the method chosen, Bunker Hills will become a settlement option afterwards, with its workbench unlocked towards the Sole Survivor.
Note: You MUST speak to Kessler to get rights to use the workbench at Bunker Hill to make it your settlement otherwise you will not be able to use the workbench.
During the battle, the residents of Bunker Hill will be seen fleeing, and all quest givers will have been temporarily moved, meaning that there is no risk towards quests being failed due to dying quest givers.