Step 1: Carbanion Stability
The stability of a carbanion depends on the ability of the negative charge to delocalize.
Electron-withdrawing groups such as nitro (\(O_2N\)) stabilize the carbanion by stabilizing the negative charge through resonance.
Step 2: Explanation of Other Options
Option (a), (b), and (c) have ethyl or methyl groups which are electron-donating and hence do not stabilize the carbanion effectively.
Option (d) with the nitro group (electron-withdrawing) attached to the benzene ring provides greater stability to the carbanion.
Step 3: Conclusion
Thus, the most stable carbanion is the one with the nitro group attached (option d).