The correct order of the second ionization potential of carbon, nitrogen, oxygen and fluorine is

$I{E}_2$ of neutral element is  $I{E}_1$ of cation having single positive charge. Hence, for order of  $I{E}_2$, first put +1 charge to each element then write electronic configuration.

$\underset{1s^{2}2s^{2}2p^6}{C^{+}}\underset{1s^{2}2s^{2}2p^2}{N^{+}}\underset{\begin{array}{l}\uparrow \\ \text{Half filled}\end{array}}{\underset{1s^{2}2s^{2}2p^3}{O^{+}}}\underset{1s^{2}2s^{2}2p^4}{F^{+}}$

From left to right in a period,  $I{E}_1$ increases and fulfilled or half filled elements have greater $I{E}_1$ than adjacent elements. Hence, correct order of  $I{E}_2$ is: C > N > F > O.