More or less the fastest possible is beginner to 2000 in 2 years. I've seen a few do it a little faster... as in 1.75 years or something. Even people like Kasparov took ~2 years (although 2000 FIDE is more impressive than 2000 chess.com).
You're not a beginner, but 1200 blitz is still far away from 2000. Two years would still be an ambitious goal. 6 months is just silly.
Just for fun I looked at a few members who covered that same ground, and just ballparking I'd put the amount of time they spent on chess.com (games, puzzles, etc) at about 2000 hours... and 2000 hours in 6 months works out to be about 11 hours a day, every day... and since marathon studying is always less efficient, you'd probably want to be safe and go for the full 16 hours a day.
My blitz rating is 1150-1200 right now and i have been playing chess for little bit less than 3 month. how much work is gonna needed to reach 2000 in 6 month or is it possible