This question asks for the exact historical year in which the Kalinga War, fought between Emperor Ashoka of the Mauryan Empire and the state of Kalinga, took place. Let's examine each of the given years against the historical record to identify the correct one.
Working from Ashoka's own regnal-year count in his edicts, only the year 261 BC lines up with the eighth year of his reign, when the Kalinga War is recorded to have taken place.
Therefore, the correct answer is 261 BC.