We have the next equation
Barium sulfate + aluminum phosphate barium phosphate + aluminum sulfate
1. We must write the skeleton equation
To write the skeleton equation we must use the next
Barium sulfate: BaSO4
aluminum phosphate: AlPO4
barium phosphate: Ba3(PO4)2
aluminum sulfate: Al2(SO4)3
Then, the skeleton equation would be
BaSO4 + AlPO4 Ba3(PO4)2 + Al2(SO4)3
2. We must balance the equation
So, if we need the same number of atoms of each type pn both sides of the equation, the balanced equations would be
3BaSO4 + 2AlPO4 Ba3(PO4)2 + Al2(SO4)3