Step 1: Recall the trend of second ionization enthalpy.
Second ionization enthalpy increases across a period from left to right due to increasing nuclear charge and decreasing atomic size.
Step 2: Analyze elements given.
The elements O, F, N, C are all in the second period. Their second ionization enthalpies generally follow:
\[
O \gt F \gt N \gt C
\]
because oxygen and fluorine have more effective nuclear charge than nitrogen and carbon, thus requiring more energy to remove the second electron.
Step 3: Conclusion.
Therefore, the correct decreasing order of second ionization enthalpies is
\[
O \gt F \gt N \gt C
\]