As we move across a period, effective nuclear charge $\left(Z_{\text {eff }}\right)$ increases and so do the first ionisation energy, $\mathrm{F}>\mathrm{O}>\mathrm{N}>\mathrm{C}$.
But after the removal of 1 electron, the second ionisation potential of oxygen becomes more than that of $\mathrm{F}$ as it acquires a half-filled stable electronic configuration. So, the correct order of second ionisation potential is $\mathrm{O}>\mathrm{F}>\mathrm{N}>\mathrm{C}$.