Strongest conjugate base among the following is

The strongest conjugate base should have the weakest conjugate acid. According to options,

${\mathrm{F}}^{-}$comes from HF which is a strong acid and ${\mathrm{OH}}^{-} \mathrm{and} {\mathrm{ClO}}_4^{-}$conjugate acid are ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{HClO}}_4$which are strong relative to ${\mathrm{NH}}_3$ whose conjugate base is ${\mathrm{NH}}_2^{-}.$ Hence,${\mathrm{NH}}_2^{-}$ is a strongest conjugate base.