Question

When would there be only four different equations for a set of math mountain numbers?

Answer 1

Only when any equation you find among those numbers can be simplified into one of the four main equations, wich means you only have four different true statements, and lots of equivalences.

Answer 2

Only when any equation you find among those numbers can be simplified into one of the four main equations, which means you only have four different true statements and lots of equivalences.
For example, 
20 + 20 = 40
40 - 20 = 20
40 = 20 + 20
20 = 40 - 20.
As the two addends are the same, so there would be only four different equations for a set of math mountain numbers.