The balanced chemical reaction is :
2HC2H3O2 (aq) +Ba(OH)2 (aq) --> 2H2O (l) +Ba(C2H3O2)2 (aq)
We are given the amount of HC2H3O2 to be used in the reaction. This will be the starting point for our calculations.
0.461 mol HC2H3O2 ( 1 mol Ba(OH)2 / 2 mol HC2H3O2) = 0.231 mol Ba(OH)2