How can an amphoteric oxide react with both acids and bases?

An amphoteric oxide is a chemical compound that can behave as either an acid or a base, allowing it to dissolve in both acidic and basic solutions. The term is derived from the Greek word amphoteros, meaning "in both ways".12

These compounds exhibit this dual nature because they can react with acids to form salts and water, and they can also react with bases to yield salts and water. For example, vanadium oxide ($V{O}_2$) acts as an amphoteric oxide: it dissolves in acid to produce the vanadyl ion ($[VO{]}^{2+}$) and reacts with base to form the hypovanadate ion ($[V_4{O}_9{]}^{2-}$).12

In the periodic table, amphoterism is primarily observed among the oxides of metalloidal elements or their close neighbors. While ionic metal oxides are typically basic and nonmetal oxides are generally acidic, amphoteric oxides often possess intermediate properties, frequently associated with elements having a +4 oxidation state.13