First off, what makes an element chemically stable? A full shell of electrons, right? This is why chlorine takes an electron to form Argon, and why sodium gives one up to become neon. The presence of that unpaired electron causes instability and instability does not release energy. (However when that unstable situation then becomes stable, a great deal of energy is released, so the formation of stability liberates more energy and the formation of instability requires energy).
So let's take a look at each situation:
A): You have Be gaining an electron and putting a lone e- in its 2p orbital. This leaves it with an unpaired electron AND a negative charge. That's not too stable.
B): You have Nitrogen gaining an electron and putting it in its 2p orbital leaving you with two unpaired electrons. All of the 2p shells, however, are of equal energy. So if the 2px, 2py, and 2pz subshells each have the same number of electrons in there, a bit of stability exists as all of the electrons in the 2p shell are feeling the same effects and are essentially equal. In the question, you're adding another electron which breaks up this stability by filling up one of the 2p shubshells. As a result, instability exists.
C): You're taking Carbon with 2 unpaired 2p electrons and adding a third electron. The carbon atom now has three electrons in its 2p shell and gains the same electron configuration as the Nitrogen started with in part B. You now have three, essentially equal electrons in the 2p shell. This provides a bit of stability to the atom. Stability releases energy.
D): You're taking Neon and adding an electron to it. To do so, you have to start filling up a higher energy 3s shell. This gives it the same electrical configuration as sodium, and we all know how reactive sodium metal is. To put another electron on Neon requires you to input a lot of energy in order to get it into that 3s subshell. This is therefore not stable.
So looking back, yes. You are correct. Option C would liberate the most energy because it forms the most stable species.