"How does one determine the A and B end on this car?"
It has correctly been pointed out that the car was to be stenciled on the "A" and "B" end as per Interchange Rule 14. An important aspect of designating the B end is contained within the rule (as shown below) for properly recording evidence of repairs.
Interchange Rule No. 14, paragraph 1: The end of the car upon which the brake shaft is located shall be known as B end and the opposite end shall be know as A end. If the car has two brake shafts the owner shall have respective ends, A and B, stenciled
on car, on both sides, near each end.
Paragraph 2: Facing the B end of car, in their order on the right side of car, wheels, journal boxes and contained parts (excluding box lids) shall be known as R1, R2, R3 and R4, and similarly those on the left side of car shall be known as L1, L2, L3
and L4. The same order of numbers shall be used for designating corresponding location of brake beams. In any case where a right or left side is designated on defect, billing repair or joint evidence cards for other parts of cars, the same uniform order
of location shall govern.