How Do 12 Year Olds Lose 40 Pounds Fast?

Well, fast is a relative term.

If you are far above your healthy weight (you can look it up if you dont know, its determined by your height/age) then you will be able to lose some of the weight relatively fast. And the rest will be a slower go.

I DO NOT recommend a "crash" diet, especially at that age. It can be extremely dangerous.

At 12 you need to ask yourself, is this a health issue or a personal image issue. If your not overweight don't worry about it.
If you are overweight then I recommend a small lifestyle change this will help you keep it off after you lose it.

Eat breakfast everyday, eggs, and a vegetable, tomato, potato, etc.
Eat an apple everyday for a snack at about 10am.
Have a healthy lunch, like a sandwich you made yourself and a fruit.
Have a snack after school, something with not much sugar, once again i prefer a fruit. Or better yet a dried fruit, it will taste like candy but still be good for you.
Have a dinner long before you go to bed. Take a short walk after dinner this will help you work of the meal.

With all the meals, eat slowly this will help our body realize that it is full and you wont eat as much. Also, slowly reduce your serving size and don't take seconds.

If you wont to lose the weight fast, cut out the meat. Replace it with tofu or another soy based product.