In the redox reaction $\mathrm{xMnO}+{\mathrm{yPbO}}_2+{\mathrm{zHNO}}_3\to {\mathrm{HMnO}}_4+\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2+{\mathrm{H}}_2\mathrm{O}$

Write the reaction in two half reactions,oxidation half and reduction half as:

Balance all atoms other than O and H.

Now balance the oxygen atoms by adding H₂​O molecules.

Now balance hydrogen atoms by adding H⁺ ions.

To balance the charge,add electrons to more positive side to equal the less positive side of the half reaction.

Now multiply oxidation half reaction by 2 and reduction half reaction by 5.Add both the reactions we will get

To change the ionic equation to original one we should add hydrogen ions equal to negative charge and nitrate ions equal to positive charge.

2MnO+5PbO₂​+8HNO₃​→2HMnO₄​+5Pb(​NO₃​)₂​+4H₂​O