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

The electronic configurations of the neutral atoms are: C ($2s^2 2p^2$), N ($2s^2 2p^3$), O ($2s^2 2p^4$), F ($2s^2 2p^5$). After losing one electron, the cations have configurations: C$^+$ ($2s^2 2p^1$), N$^+$ ($2s^2 2p^2$), O$^+$ ($2s^2 2p^3$), F$^+$ ($2s^2 2p^4$). For the second ionization enthalpy, we remove an electron from these cations. N$^+$ has a stable half-filled $2p^3$ configuration, making its second ionization enthalpy exceptionally high. Oxygen (from O$^+$, $2p^3$) also has a half-filled configuration after losing the second electron, giving it the highest value among them. Thus, the order of second ionization enthalpy is O > N > F > C.