Fallout 4 created by Bethesda Game Studios.
Images used for educational purposes only.

Prerequisites: Begin Semper Invicta
Trigger: Speak to Knight Rhys
Reward: 105 Bottlecaps, 200 XP

- Cleansing the Commonwealth is part of a larger Brotherhood of Steel quest called Semper Invicta. Once you’ve started Semper Invicta Rhys will have this quest ready for you, along with another quest for Scribe Haylen. You need to complete both of them as part of Semper Invicta.

- Cleansing the Commonwealth is a pretty damned straightforward quest, at least as far as Rhys puts it: he wants you to clear the Feral Ghouls out of… somewhere. Where he sends you is random, and all you know is that it’s crawling with Ghouls. Yay?

College Square

Your target, whatever it is, will not be friendly to your efforts. There are Ghouls hiding in buildings, on top of buildings, inside the backs of vehicles, in back rooms, and, when you’re lucky, sitting out in the open. They’re extremely quick to rush towards a fight, and you can quickly get overwhelmed by the bastards if you make too much noise. How you proceed depends on the location, but you nevertheless have a few options for proceeding:
  • Take the noisy route, but go slowly. Suit up in Power Armor and start shooting at one end of the Square, using V.A.T.S. to eliminate progressive waves of Ghouls. This will bring in plenty of Ghouls, but they should come in clusters rather than a massive swarm so long as you hold your ground. Go running willy-nilly and you’ll bring every one of the bastards down on your head.
  • Go at it stealth style. Move slowly, wait for Ghouls to show themselves, and shoot. This route takes much longer because you’ll need to hunt inside buildings and check the backs of trucks, but it’s substantially safer than running and gunning, and very easy if you get upgraded damage from Sneak Attacks. A silenced weapon is recommended.
  • Combine the two. Sneak, fire, kill Ghouls that show up, and repeat. Try to find easily-defensible positions.

Regardless of how you proceed, this quest entails killing one Ghoul in each location, rather than actually clearing out the whole thing. (It's still a good idea to kill them as you go along, to prevent them from ganging up on you.) Choose Cleansing the Commonwealth in your Pip-Boy and the Ghoul will be highlighted on the screen. Then you just need to hunt the bastard down and put a bullet, or a baseball bat, or a fist, or whatever, in its brain. The Ghoul is going to be more advanced, so watch yourself. Return to Rhys for your reward. 

Given the nature of the quest, you can complete Cleansing the Commonwealth as many times as you like, assuming you’re still friendly with the Brotherhood of Steel. (And, yes, Rhys is less of a dick once you complete enough missions. He never quite loses that edge, though.)