I agree with April, you don't want to malnutrition yourself or anything because at this point in your life it could lead to improper development and growth.
Also, I should say, its definitely possible to lose 40 lbs in 4 months healthily, but you have to be really committed to it and really strict with yourself. That means NO cheating at all! And I remember when I was 15, I certainly did not have the self-control for that kind of thing.
April, I believe she has a goal of 4 months because that's around the same time of year as Proms and other "big" events in the school year (though I think March is a little early, I thought they were around May and into June). Maybe there's another event?