How much weight can you loose running 20 minutes everyday for a week?

Unless you have your eating under control - nothing. Depending on your weight, size, gender etc, running for 20 minutes may lose you about 200 calories - that's half a cupcake's worth. For that to make a difference anytime soon you need to have your eatin really well under control.

Assuming all your eating is right on the money, then losing 200 calories/day may let you lose 1 lb/week.