pH=13.30 .

Barium hydroxide is a strong base for both stages of dissociation:

Ba(OH)2(s)→Ba2++2OH−

So the solution will have 0.20 M hydroxide ions. Now use the autodissociation product for water:

[H+][OH−]=1.0×10−14M
[OH−]=2.0×10−1M
[H+]=5.0×10−14M

And then

pH=−log10([H+]=5.0×10−14)=13.30 .