What is the correct ionic formula when mg2+ and p3− react?

Any compound should have a neutral charge. So the compound you make should have a net charge of zero.

So you have:
Mg which is 2+
And P which is 3-

You want to balance out both their charges. If you simply made MgP it would have a negative charge (because 2-3 = -1.)

Now to balance this, you have to find the LCM: In this case it is 6. (2x3)

Mg: Mg x 3
P: P × 2

You'll finally get Mg3P2.