Question

Why can’t one of the names be PNM, or MPN for the plane? But MNP can? What’s the difference, and why?

Answer 1

The names PNM and MPN are perfectly valid. The order of the letters doesn't matter. In fact, there are 6 ways to name this plane if we just use the 3 letters. If we include "plane Z", then there are 7 total ways to name the plane.

For some reason, your teacher wants P to be the third letter as s/he mentioned MNP and NMP. But again, the order doesn't matter.