How to solve this diode circuit?
You have the answer already and have asked for guidance ("But I don't know how we got there"), which is all I can give for homework questions...

Your question uses 'perfect' diodes, so no voltage drop and no leakage currents amongst other things.

Perfect diodes do not conduct when they are reverse-biased. Therefore any path that has a reverse-biased diode is open-circuit. When you're assessing the circuit, pretend that reverse-biased diode paths are not there.

Look at each diode in turn. Seeing the voltage it puts onto the resistor bottom-end, consider the effect on the other diodes.

This should take you most of the way to the answer. Then its just Ohm's Law at the end.