It's possible if you're a lard ass to start with. For example, if you start at over 16 stone (16*14 = 224 lbs = 100 Kgs) then it's possible to loose 3-4 lbs per week at the start of a diet. This is fairly normal since you're initially loosing a lot of water, this weight loss should then even out to a more sensible 1.5-2 lbs per week. So yes, it is possible to loose 20lbs in 2 months, (4weeks*3lbs)+(4weeks*2lbs).
However, if you are initially 'fit' and not seriously over weight then it's not healthy to loose more than 1.5-2 lbs per week, so here the answer would be no.
Don't eat for 4 weeks! Drink Guiness to replenish your Iron. Drink lemon juice for Vit C. Eat loadsa chicken breasts unfried and oven cooked. You'll do it! And eat the odd pulses or wheat to feed your brain. (otherwise ask a GP! or an anorexic, I wouldn't do the latter - you may feel fat after 4 weeks)
Yes it is possible. Used to be a wrestler and a kid lost 55 pounds over 3 months. He wasn't in really good shape I mean he had some fat but still. But it wasn't a healthy diet he barely ate and ran all the time. 20 pounds in 2 months is quite a bit if you're already in good shape. If your body fat % is below 10 that will be quite hard.