I am 5'2 and I weight about 116-120 pounds, I'm not over weight but I not skinny, I'm athletically built and I have big thighs and arms. If I stick to taking in 1,200 calories a day and exercising how much weight will I lose in 3 months?

Depends on how much you exercise, but maybe 5 pounds. You really don't have all that much to healthily lose.