You'll easily be able to lose 12 pounds over 28 days - you will get a rapid weight loss in the first two weeks, but it'll be primarily food and water weight, especially as you're limiting your calories and not eating.
I've used the Velocity Training Programme - with my own adaptations - for a while, and it's great for adding lean mass, and followed whilst following the Velocity Diet, should yield good results. After your training, it is going to seem a lot LESS, considering that the resistance sessions only take 15-25 minutes to complete. The V-Burn Challenge Circuit takes ~40 minutes to complete. The Velocity Training Programme ONLY includes FOUR days of a single training session per day - no added cardio.
You do know that following this will NOT spot reduce the fat on your butt or abs, but you WILL lose fat from ALL OVER, which should reduce those areas.
The Primordial Woman