NASCAR The Game 2011

I would recommend setting race difficulty settings with the AI on easy.

You will get 250pts a lap from leading it, as well as 100-200pts for dominating. If you race at bristol, you'll get points for lapping cars as well.
You'll get 30 points for every lapped car you pass. Also, if you don't qualify and start 43rd, you'll get 10-50 points per pass for every car until you reach first place, as long as they were clean passes. You also get additional bonus points for taking the lead.

Make the race about 10% or so. It doesn't matter which track. You'll just have to be patient and you'll easily earn the NXP over time. It's an easy achievement, but it takes time to get.

Good Luck!

I did this in Invitational Challenge, Pocono Gauntlet.
First the challenge is run in two stages so you have to race twice.

So put the game on easy if not already.

After you win the first round you will start at the back of the pack just take it easy and pass as many people as cleanly as possible, lead as many laps as possible and win. It shouldnt be too hard.

I did this my first try and wasnt even trying to get this achievement. If you vote negative please tell me why thanks.

You get 250 NXP for leading one lap, so to pass 6,666 it would take 27 laps (27*250 = 6,750). Do a race about 25 laps (any track) and you should easily get it (along with the burnout bonus) as long as you win. I did this in a 30 lap race at Kansas.