Hydrochloric acid (12.0 ml of 0.233 m) is added to 296.0 ml of 0.0579 m ba(oh)2 solution. what is the concentration of the excess h+ or oh − ions left in this solution?

The balanced equation for the reaction is as follows;
Ba(OH)₂ + 2HCl ---> BaCl₂ + 2H₂O
stoichiometry of  base to acid is 1:2
Ba(OH)₂ is a strong acid and HCl is a strong base therefore complete ionization takes place
the number of HCl moles reacted - 0.233 mol/L x 0.0120 L = 0.00280 mol
number of Ba(OH)₂ moles reacted - 0.0579 mol/L x 0.2960 L = 0.0171 mol
we have to first find the limiting reactant 
if HCl is the limiting reactant 
if 2 mol of HCl reacts with 1 mol of Ba(OH)₂
then 0.00280 mol of HCl reacts with -0.00280 / 2 = 0.00140 mol of Ba(OH)₂
and 0.0171 mol of Ba(OH)₂ is present, therefore Ba(OH)₂ is in excess and HCl is the limiting reactant 

number of excess Ba(OH)₂ moles = 0.0171 - 0.00140 = 0.0157 mol
total volume - 12.0 mL + 296.0 mL  = 308.0 mL
[Ba(OH)₂] = 0.0157 mol / 0.3080 L = 0.0510 M
since Ba(OH)₂ is a strong acid
Ba(OH)₂ --> Ba²⁺  + 2OH⁻
therefore [OH⁻] = 2[Ba(OH)₂]
[OH⁻] = 2 x 0.0510 = 0.102 M
hydroxide ion concentration is 0.102 M