You bought 6 packages of hot dogs.
To solve this, you have to write and solve a system of equations. Let B stand for hamburgers and H stand for hot dogs.
B + H = 11
8B + 2H = 52 If you multiply the top equation by -2, you can solve by eliminatoin.
-2B + -2H = -22
8B + 2H = 52 Add the equations
6B = 30
B = 5
If you bought 5 packages of hamburgers, then you bought 6 packages of hot doges. 11 - 5 = 6