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We need to find the total amount of liquid in the system at the equivalence point. 100 mL of 0.2 M acetic acid has 0.02 moles of acetic acid. For every mole of acid we need half the number of moles of Ba(OH)2 since there are two moles of OH per mole of the base. So we need 0.01 moles of Ba(OH)2 to reach the equivalence point. This would mean that we need 0.01/0.04 = 0.25 liters or 250 mL of base solution. So this is a total of 100 mL + 250 mL = 350 mL. That means 350 mL is the final volume at the equivalence point.
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