Step 1: Recall the trend of second ionization enthalpy.
Second ionization enthalpy increases across a period due to increasing nuclear charge and decreases down a group due to increasing atomic size.
Step 2: Analyze the elements given.
Among Carbon, Phosphorus, Nitrogen, and Oxygen, the elements are in periods 2 and 3. Oxygen (period 2, group 16) has the highest effective nuclear charge and smallest size, making its second ionization enthalpy the highest.
Step 3: Conclusion.
Thus, the element with the highest second ionization enthalpy is Oxygen.