The correct option is C O > F > N > C
After the removal of an electron from C, N, O and F their electronic configurations are:
C+ - 1s2 2s2 2p1
N+ - 1s2 2s2 2p2
O+ - 1s2 2s2 2px1 2py1 2pz1
F+ - 1s2 2s2 2px2 2py1 2pz1
Since O+ gives a stable electronic configuration with exactly half-filled 2 p-sub shell, therefore, 2nd ionization enthalpy of O is higher that of F. The 2nd ionization enthalpy of C is lower than that of N because of its larger size.
Thus, the overall order is O > F > N > C .