To balance the skeleton equation ( \text{Al}_2(\text{SO}_4)_3(aq) + \text{KOH}(aq) \rightarrow \text{Al(OH)}_3(aq) + \text{K}_2\text{SO}_4(aq) ), the coefficients needed are 2 for KOH, 1 for ( \text{Al}_2(\text{SO}_4)_3 ), 2 for ( \text{Al(OH)}_3 ), and 3 for ( \text{K}_2\text{SO}_4 ). Thus, the balanced equation is:
[ 1 \text{Al}_2(\text{SO}_4)_3 + 6 \text{KOH} \rightarrow 2 \text{Al(OH)}_3 + 3 \text{K}_2\text{SO}_4 ].