In order to build the souped-up version of starter rifle the Khvostov – check out How to Get the Khvostov 7G-OX to get started as well as How to Get and Use Splicer Keys, Splicer Intel Relays, and SIVA Offerings for how to actually find the start of the quest – you'll eventually need to find 10 Manual Pages and three Khvostov Parts after getting the quest I Found A Rifle. The Manual Pages can be acquired by killing enemies during a patrol of The Plaguelands, but the Khvostov Parts are scattered in locations near the Rocketyard. Here's how to find all the Khvostov Parts.
To start, begin a Patrol in The Plaguelands. From the spawn point at Lord's Watch, go forward until you make it to a large building on the right with glowing orange scratch marks all over it. Follow the glowing orange marks to the Rocketyard. We're going to use the Rocketyard as a starting point to finding the parts, as all three can be found down both diverging paths from the Rocketyard. Note that they're all found in areas previously seen in Old Russia:
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One of the Parts is in the Refinery on the path towards The Blast, which you can get to by turning left after emerging into the Rocketyard from Lord's Watch. Just before you get to The Blast, you'll see a platform with orange walls and pipes on the right. The Khvostov Part is in the corner on that platform. Note that this path is the same one that you follow during The Devil's Lair Strike.
Emerging outside into The Blast from the building that leads back to the Refinery, you'll see a small building directly in front of you. On the far side of it facing the enemy Walker and the way to Devil's Lair, you'll find the part nestled in a corner between two pieces of machinery. Remember that it's outside the building around the corner of its perimeter. And again, this is on the same path as The Devil's Lair Strike, so if you've completed that run, then you should be familiar with the branch containing the Refinery and The Blast.
The third Part is down the other path branching off of the Rocketyard, into The Divide. From the Refinery, it's a straight shot to The Divide. From Lord's Watch, it's to the right of where you emerge from the destroyed building. Once you get to The Divide, take the downhill path towards Dock 13. Make your way to the outdoor plaza area at the very end of the path and start searching the rooms that branch off from the plaza. The Khvostov Part is in one of the enemy spawn rooms leading from the plaza underneath some stairs.
Once you've found all the Khvostov Parts and Manual Pages, go back to the Iron Temple and talk to Shiro-4 to continue the questline that gets you the Khvostov 7G-OX. To see what to do from here, don't forget to check out How to Get the Khvostov 7G-OX.