Attach FMJ to the weapon you are trying to complete the challenge with.
Then follow an enemy with your fire as they run for cover.
Or otherwise try to get them behind cover once they are hiding.
Often, you can easily spot someone behind a window or a wall when the barrel of their weapon is sticking out.
Easiest to shoot through is sheet metal like the most walls on Scrapyard.
gaming.stackexchange.com/users/178/Dmitry Selitskiy
An extremely easy and fast way to get Bullet Penetration kills is to play 3rd person team tactical.
When you aim down your sights, you look over your right shoulder, so if you are on the left side of a door and you aim down your sights, you can see down the hallway and not be seen by anyone in that hallway.
Let your guns go and fire through the wall for the easiest Bullet Penetration kills.
gaming.stackexchange.com/users/10563/Nooge-22
Just what the name implies really.
It's counted as a bullet penetration kill when you kill someone who's behind a wall (even shooting through a railing can count), all while using the FMJ attachment.
It's probably the trickiest challenge to complete with any gun (certainly with sniper rifles).
Tip: When you see someone who's trying to run for cover, you've got a choice whether to for the chase or to shoot.
In this case, shoot them through the wall.
Doing this however will give your position away to your enemy.
gaming.stackexchange.com/users/172/happy_soil
You have to shoot and kill people that are behind something, like a thin wall.
Also make sure you have the FMJ attachment active on the weapon you are using, or it won't count as a kill in the challenge.
gaming.stackexchange.com/users/154/sippa
An easy way to obtain FMJ kills is by shooting through glass at your enemies.
Some good levels for FMJ kills are Highrise, Terminal, Trailer Park (new map), Scrapyard.
gaming.stackexchange.com/users/318/DarkShiva
Equip FMJ and the heartbeat sensor using Bling.
This won't work for sub machine guns obviously.
Stopping power is important as well.
Play hardcore game modes.
Objective ones are sometimes better.
Basically stalk around the outside of buildings.
When you see a red blip, line up your shot and start firing.
If you don't immediately get hit markers then start making small sweeps.
If you are playing an objective game then your best bet is to assume they are prone next to the objective.
gaming.stackexchange.com/users/745/colithium
Some kills through fences will count as BP kills.
I think it depends on whether or not you catch part of the fence (though I could be wrong).
I usually do pretty well racking up BP kills on Scrapyard (there's a good fence in where the B flag is in domination) or Sub Base (in the room with the fenced in generator).
Shooting through fences or glass is nice in that it eliminates some of the guess work.
Fences are nice in that you get to shoot through them more than once (even though it doesn't always work).
Another option is to shoot through the mattresses in Skid Row from either end of the long hallway.
In domination this is where the B flag is.
This is nice as the enemy is in a fairly predictable location on the other side of a pretty thin obstacle.
I've also gotten a fair amount by hiding behind a barricade.
The ideal situation is where you can stand and shoot the enemy directly.
When you see them you just duck behind the barricade and shoot through it.
If you're still having trouble, try using Bling with a heartbeat sensor as well.
That helps a fair amount with the ARs in knowing where to shoot in a lot more cases.
gaming.stackexchange.com/users/636/Robert Simmons
As the others have posted you need to kill someone using FMJ whilst shooting through a wall.
The point I was going to make is that the reward is not Unlimited mags but Extended mags.
gaming.stackexchange.com/users/None/
What do you have to do to get a bullet penetration kill in MW2?  I've been stuck trying to complete the extended mags challenges because I'm not getting the penetration kills required.
How to get bullet penetration kills in MW2?
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gaming.stackexchange.com/questions/500
gaming.stackexchange.com/users/43/squillman
Attach FMJ to the weapon or play 3rd person team tactical. It counts when you get a kill by shooting through something, like a glass wall.  It's counted as a bullet penetration kill when you kill someone who's behind something, like a wall or glass, while using the FMJ attachment.  Some kills through fences will count as BP kills.  You need to make sure you have the FMJ attachment active on the weapon you are using, or it won't count as a kill in the challenge. An extremely easy and fast way to get Bullet Penetration kills is to play 3rd person team tactical.  
Attach FMJ to the weapon you are trying to complete the challenge with. An extremely easy and fast way to get Bullet Penetration kills is to play 3rd person team tactical.    It's counted as a bullet penetration kill when you kill someone who's behind something, like a wall or glass, while using the FMJ attachment.  Some kills through fences will count as BP kills.   You need to make sure you have the FMJ attachment active on the weapon you are using, or it won't count as a kill in the challenge.