The Battle of Bunker Hill

The Battle of Bunker Hill is an Institute main quest in Fallout 4.

Detailed walkthrough
Father wants you to go to Bunker Hill to send some escaped synths back inside The Institute. You will meet up with Courser X4-18 who is going to teleport them back. Bunker Hill is under protection of the Railroad, a group of people who help runaway synths. You can optionally inform Desdemona that the Institute are coming to get their synths back, that way they are prepared. You can also optionally inform Elder Maxson about the attack. If you have talked to both Desdemona and Maxson, X4-18 will be suspicious of your lateness, causing it to call for backup.

When the battle starts, and if you were to report the Battle to either the Brotherhood or the Railroad, a large firefight will erupt in and around the settlement. The main doorway into the settlement is locked, requiring the Sole Survivor to walk around and head to the right-side of the settlement where an opened door can be found. Alternatively, the trailer next to the locked gate makes a handy bridge. The inhabitants of Bunker Hill will cower during this firefight, and will most likely not get killed by either the Synths, Brotherhood or the Railroad.

Once inside Bunker Hill, there should be a small doorway into a basement where you will find the runaway synths Z3-22, B2-57, Y9-15 and F6-33. Should X4-18 still be with you once you've reached the synths, you've got the choice to let them go or capture them. Choosing the former will force X4-18 to go hostile. A new objective will be added where you are to talk to Father on the roof of the ruins of C.I.T. There you will have to talk to Father and explain your actions at Bunker Hill. From here, you have a choice to choose if you want to still be a part of the Institute.

Behind the scenes
The title of this quest is a reference to the historical Battle of Bunker Hill, an important conflict of the American Revolutionary War occurring near Bunker Hill in 1775.
 * Contrary to popular belief, the bulk of the fighting during the Battle of Bunker Hill took place at the site of the American redoubt on Breed's Hill, not Bunker Hill. The Bunker Hill Monument was erected at the site of the battle, on the peak of Breed's Hill. Thus, both historically and in-game, the Battle of Bunker Hill takes place on Breed's Hill, not Bunker Hill.

Bugs
La batalla de Bunker Hill Битва за Банкер-Хилл