Derivation and application of the Henderson-Hasselbalch equation
The reaction taking place is the quantitative reaction:
$$\ce{AH + OH- -&gt; A- + H2O}$$ 

The initial concentrations are:
 $$\ce{[OH- ]_0}=\frac{0.001}{0.1}=0.01  \mathrm{M}$$  $$\ce{[AH ]_0}=\frac{0.002}{0.1}=0.02 \mathrm{M}$$
The equilibrium concentrations:
 $$\ce{[AH ]}=\frac{0.002-0.001}{0.1}=0.01 \mathrm{M}$$ 
 $$\ce{[OH- ]}=10^{-8}  \mathrm{M}$$
 $$\ce{[A- ]}=0.02-0.01=0.01 \mathrm{M}$$ 
Using the equation of question (ii):

$\ce{pH = p}K_a=6$