In the general plan for balancing redox equations, when a reaction takes place in basic solution, you will need to add

Answer is: add hydroxide ions (OH⁻).
For example unbalanced chemical reaction:
H₂O₂(aq) + Cl₂O₇(aq) → ClO₂⁻(aq) + O₂(g).
Reduction half reaction: 6H⁺  + Cl₂O₇ → 2ClO₂⁻ + 3H₂O.
Oxidation half reaction: H₂O₂ → O₂ + 2H⁺ + 2e⁻ /×4; 4H₂O₂ → 4O₂ + 8H⁺ + 2e⁻
Sum: 6H⁺ + Cl₂O₇ + 4H₂O₂ → 4O₂ + 8H⁺ + 2ClO₂⁻ + 3H₂O;
Cl₂O₇ + 4H₂O₂ → 4O₂ + 2H⁺ + 2ClO₂⁻ + 3H₂O
Add 2 OH⁻: 2OH⁻ + Cl₂O₇ + 4H₂O₂ + → 4O₂ + 2ClO₂⁻ + 5H₂O.
Balanced chemical reaction: 4H₂O₂ + Cl₂O₇ + 2OH⁻→ 2ClO₂⁻ + 4O₂ +5H₂O.