To balance the following chemical equation, make a tally or a count of each of the atoms on both sides of the reaction, and make sure that those atoms are equal on both the reactant and product side. 
AL2O3 + HCl => ALCl3 + H2O 
Left side. Right side
AL = 2. AL = 1
O = 3 Cl = 3
H = 1. H = 2 
Cl = 1. O = 1 
First balance the metal atoms, aluminum, then hydrogen and then oxygen. 
Balanced equation :
AL2O3 + 6HCl => 2ALCl3 + 3H2O. 
Left side. Right side 
AL = 2 AL = 2 
O = 3 Cl = 6 
H = 6 H = 6 
Cl = 6 O = 3.