In the reaction, Cu changes its oxidation number from 0 to +2. The net change in the oxidation number is 2.
N changes its oxidation number from +5 to +4. The net change in the oxidation number is 1.
Hence, to balance the net increase in the oxidation number of Cu with net decrease in the oxidation number of N, the nitrate ion and NO2 is multiplied with coefficient 2.
Cu+2NO⊖3⟶2NO2+Cu2+
The balanced chemical equation is as follows:
Cu+2NO⊖3+4H+⟶2NO2+Cu2++2H2O