Since phosphoric acid is made up of radical phosphate (PO4) with valence 3- and hydrogen having valence 1+ its chemical formula need to be H3(PO4).
Since Lithium hydroxide is made up of radical (OH) having valence 1- and Lithium having valence 1+ its chemical formula need to be Li(OH).
Now we write the unbalanced chemical equation of the acid-base reaction as
H3(PO4) + Li(OH) = H2O + Li3(PO4)
Before balancing the equation we need to deduct the reaction products. First product is always water H2O, second reaction product is the salt made from the metal that composes the initial hydroxide (Li) and the radical that composes the initial acid. Hence the chemical formula is Li3(PO4) and its name is lithium phosphate, taking into account the above mentioned valences of Li -(1+) and (PO4) -(3-).
Now we need to balance the equation.
First we number the atoms of Li. One atom entering, 3 atoms resulting. Therefore we multiply the number of molecules of hydroxide (containing Li) with 3.
Now we number the atoms of Hydrogen. Atoms of Hydrogen entering is 6, atoms of hydrogen resulting 2. So you multiply the resulting molecules of H2O (the only reaction product that contain Hydrogen) with 3.
We next number the atoms of O and P that enters and result from the reaction and see their number is the same (7 atoms of O and 1 atom of P).
Now we can write the balanced equation in the form:
H3(PO4) + 3*Li(OH) = 3*H2O + Li3(PO4)