The correct answer is option 2: Kochi. The headquarters of the Southern Naval Command is located in Kochi, a city in the state of Kerala, India. It is one of the three main naval commands in the Indian Navy, along with the Western Naval Command in Mumbai and the Eastern Naval Command in Visakhapatnam.

Option 1, Arakkonam, is not the correct answer. Arakkonam is a town in the state of Tamil Nadu, India and does not house the headquarters of the Southern Naval Command.

Option 3, Thiruvananthapuram, is also not the correct answer. Thiruvananthapuram is the capital city of Kerala, but it does not serve as the headquarters of the Southern Naval Command.

Option 4, Visakhapatnam, is also a major naval command, but it is the location of the Eastern Naval Command, not the Southern Naval Command. Therefore, it is not the correct answer.

In conclusion, the correct answer is option 2: Kochi, as it is the location of the headquarters of the Southern Naval Command.