For a substance to be called amphoteric, it should be able to react as a base as well as an acid. Hence, when it is reacted with a base, it should act as an acid, and when it is reacted with an acid, it should behave as a base.
The reactions for amphoteric nature of Al2O3. x H2O(s) are
Al2O3.xH2O(s)→OHaq−Al(OH)4−aq
Aluminate anion
Al2O3.xH2O(s)→Haq+[Al(H2O)6]aq3+.
[Al(H2O)6]3+ is octahedral complex ion
[Al(OH)4]−1 tetrahedral at pH = 13