I don't understand how you know what state designation things are in a chemical equation. For example this is given:

2 (NH4)3PO4 (__) + 3 Ba(NO3)2 ---> Ba3(PO4)2 (__) + 6 NH4NO3 (__)

How do you just know what to put for their state or phase designation?

You have to be given something. If the original reactants were in solution in water, then the first two are (aq). But is Barium phosphate soluble in water (NO), so it is (s). Ammonium nitrate is soluble, so it is (aq)