Answer
We can rank the situations according to the magnitude of the net electric field:
$(1) = (2) \gt (3)$
Work Step by Step
We can consider the electric field at point $P_3$
In case (1), the electric field from Ring A is directed to the right, while the electric field from Ring B is directed to the right. The magnitude of the net electric field is the sum of the magnitudes of the electric field due to Ring A and the electric field due to Ring B.
In case (2), the electric field from Ring A is directed to the left, while the electric field from Ring B is directed to the right. The magnitude of the net electric field is the sum of the magnitudes of the electric field due to Ring A and the electric field due to Ring B. Note that the magnitudes of the electric fields due to Ring A and Ring B are that same as in case (1), but point in the opposite direction.
In case (3), the electric field from Ring A is directed to the left, while the electric field from Ring B is directed to the right. The magnitude of the net electric field is the difference of the magnitudes of the electric field due to Ring A and the electric field due to Ring B.
We can rank the situations according to the magnitude of the net electric field:
$(1) = (2) \gt (3)$