The answer is, 4 + 8 + 12 + 16 ... rule is 4n.
Explanation:
one square has 4 toothpicks, then you added 4 picks (because you started with zero squares).
4 squares have 12 toothpicks, then you added 8 toothpicks to pass from one square to 4 squeres.
If you follow that reasoing you get to realize that the additions are 4, 8, 12, 16.