How can i find the axis my part is facing relative to the plot

i’ve been struggling with this issue for a bit, it looks simple but i just cant comprehend how to do it, i managed to fix it but the way i did it isnt practical at all so here’s my issue
it starts out facing the correct directions but then as i press R to rotate it by 90 degrees, logically its now something like this

what do i need to do in order to see that now the Z axis is facing plots X?

I will just proceed to use the non practical way due to the lack of help provided