In order for a buffer to have pH=pKa, how many moles of the base should be added?

H2NNH2 is a base and H2NNH3NO3 is a salt of this base and strong acid HNO3  so it is a basic buffer mixture.

now when you add base it will react with salt H2NNH3NO3 since it contains the acid part HNO3 .....the base will not react with H2NNH2 ......thats why you were getting the wrong answer ....

so for NaOH rection will be :

H2NNH3NO3 + NaOH --------> H2NNH2 + NaNO3 + H2O

so let x moles of NaOH be added

then new no.of moles of H2NNH2 = 0.4 + x
and new no.of moles of H2NNH3NO3 = 0.8-x

and pH= pKa + log [base]/[acid]

8.22 = 8.22 + log 0.4+x / 0.8-x

1 = log 0.4+x/0.8-x

0.4+x = 0.8-x

2x = 0.8-0.4

x = 0.4/2 = 0.2 moles

feel free to ask any questions