How the rule works
Two cells are laid on top of each other, and only what is present in both remains: edge lines, filled sectors or arrows that both cells have. Anything only one of them has disappears. The rule holds along rows and along columns at the same time, so the bottom right cell can be worked out two ways, and they must agree.
The rule is a sibling of patterns combined and patterns cancelling out. The difference shows in the third cell: if it is poorer than both of the first two it is the intersection, if it is richer it is the union, and if the shared part is gone but the rest remains they cancel out.