Answer
2$H_{3}PO_{4}$ (aq) + 3 Mg$(OH)_{2}$ (s) $\longrightarrow$ $Mg_{3}$$(PO_{4})_2$(s) + 6$H_{2}$O(aq)
Work Step by Step
First we have to write chemical formula for the compounds in this chemical reaction:
$H_{3}PO_{4}$ (aq) is the chemical formula and the state symbol for oxacid that contains phosphate anion.
Mg$(OH)_{2}$ (s) is the chemical formula and the state symbol for solid magnesium hydroxide.
$H_{2}$O(aq) is the chemical formula and the state symbol for dihydrogen monoxide.
$Mg_{3}$$(PO_{4})_2$(s) is the chemical formula and the state symbol for the solid ionic compound formed from the combination of magnesium cations and phosphate anions.
The chemical reaction is:
$H_{3}PO_{4}$ (aq) + Mg$(OH)_{2}$ (s) $\longrightarrow$ $Mg_{3}$$(PO_{4})_2$(s) + $H_{2}$O(aq)
Balance Mg by adding 3 before Mg$(OH)_{2}$
$H_{3}PO_{4}$ (aq) + 3 Mg$(OH)_{2}$ (s) $\longrightarrow$ $Mg_{3}$$(PO_{4})_2$(s) + $H_{2}$O(aq)
Balance P by adding 2 before $H_{3}PO_{4}$ (aq)
2$H_{3}PO_{4}$ (aq) + 3 Mg$(OH)_{2}$ (s) $\longrightarrow$ $Mg_{3}$$(PO_{4})_2$(s) + $H_{2}$O(aq)
We count that there are 12 atoms H on the left ( 3x2 + 3x2) and only 2 on the right. Add 6 before $H_{2}$O(aq)
2$H_{3}PO_{4}$ (aq) + 3 Mg$(OH)_{2}$ (s) $\longrightarrow$ $Mg_{3}$$(PO_{4})_2$(s) + 6$H_{2}$O(aq)
We see that we have balanced O atoms as well. There are 14 on the left ( 2x4 + 3x2) and 18 on the right ( 4x2 + 6) .
We have balanced all atoms in the above chemical equation.
