Balancing a chemical equation involves putting appropriate coefficients on the reactants and products to make the number of atoms of each element involved equal on both sides of the equation.
When a chemical equation is balanced then it obeys the law of conservation of mass.
The law of conservation of mass requires the mass of reactants to be equal to the mass of the products.
In this case, to balance the equation, we put the coefficients 1, 4, 2, 1 and 2 receptively on the equation.
Thus, the balanced equation will be;
Pb₃O₄ + 4HNO₃ → 2Pb(NO₃)₂ + PbO₂ + 2H₂O\
Therefore, on the reactants side there are 3 Pb atoms, 16 O atoms, 4 H atoms and 4 nitrogen atoms.
Product side : 3 Pb atoms, 16 O atoms, 4 H atoms and 4 nitrogen atoms.
Thus, the equation obeys the law of conservation of mass.