Since a dozen has 12 eggs, the total number of eggs that Addilynn bought is 6 dozen * 12 eggs/dozen = <<6*12=72>>72 eggs.
If she used half of the eggs, the number of eggs left is 72 eggs / 2 = <<72/2=36>>36 eggs.
While moving the eggs to clean the shelves, she broke 15 eggs, leaving 36 eggs - 15 eggs = <<36-15=21>>21 eggs.
#### 21