A bar is level when weight × distance is the same on both sides. The distance is the number of notches from the pivot to the hook, also written above each arm. A side's weight is everything hanging below it.
Tap a weight, then another to swap them. Undo takes a swap back, and the swap still counts.
A bar that is out of balance leans toward its heavy side, always by the same amount: a lean says which side is heavy, not by how much.
Fewest is the swaps the day's scramble needs. Start from the top bar: it decides what each half must weigh.