K3PO4 (aq) + AlCl3 (aq) -> 3KCl (aq) + AlPO4 (s)
That is a double replacement reaction
K3^+1 (aq) + PO4^-3 (aq) + Al^+3 (aq) + Cl3^-1 (aq) -> 3K^+1 (aq) + 3Cl^-1 (aq) + Al^+3 (s) + PO4^-3 (s)
This is the total ionic equation, to find that we need to know and write down the charges of all the elements, and not just the charges but also the state of every element.
Al^+3 (aq) + PO4^-3 (aq) -> AlPO4 (s)
The net equation only needs the ions that are playing an important role in the reaction, either by changing charges or changing states, we see in this reaction both Al and PO4 are changing states, so they will be in the net equation