The dissociation of this basic compound is: [tex]Ba(OH)_2\ \to\ Ba^{2+} + 2OH^-[/tex]
There will be the double of [tex]OH^-[/tex] ions than molecules of [tex]Ba(OH)_2[/tex], therefore, the concentration of [tex]OH^-[/tex] at the end will be 0.820 M.
[tex]pOH = -log\ [OH^-] = - log (0.820) = \bf 0.09[/tex]