let [NO2-]=x,
NO2- + H2O => HNO2 +OH-
initial [] x 0 0
change [] -y y y
final [] x-y y y
Kb=Kw/Ka=2.2E-11=(y^2)/(x-y)
y^2 + (2.2E-11)y - (2.2E-11)x = 0
y=(-2.2E-11 + sqr(2.2E-22 - 8.8E-11x))/2
x is the concentration of NO2-, which should be provided in the question.
plug in the concentration for x, solve for y, the concentration for OH-.
then, pH=14+log(y)
if you plug in 0.5 for x, pH is 8.52
if pH is 12.17, then x must be 9844927.323...