The half equations of the reaction are
MnO4−⟶Mn2+C2O42−⟶CO2
The balanced balf equations are
MnO4−+8H++5e−⟶Mn2++4H2OC2O42−⟶2CO2+2e−
On equating number of electrons, we get
2MnO4−+16H++10e−⟶2Mn2++8H2O5C2O42−⟶10CO2+10e−
On adding both the equations, we get
2MnO4−+5C2O4−+16H+⟶2Mn2++2×5CO2+216H2O
Thus x,y and z are 2,5 and 16 respectively.