The correct answer is option 3, Y. V. Reddy.

Option 1, C. Rangarajan, is incorrect. He served as the Chairman of the Twelfth Finance Commission, not the Fourteenth Finance Commission.

Option 2, Vijay Kelkar, is incorrect. He served as the Chairman of the Thirteenth Finance Commission, not the Fourteenth Finance Commission.

Option 4, Rakesh Mohan, is incorrect. He has not served as the Chairman of any Finance Commission.

Y. V. Reddy, who is the correct answer, served as the Chairman of the Fourteenth Finance Commission. He held this position from 2013 to 2014. The Finance Commission in India is a constitutional body that is responsible for making recommendations on the distribution of taxes between the Union government and the states. The Fourteenth Finance Commission was particularly significant as it recommended an increase in the share of states in the divisible pool of taxes, giving them more financial autonomy.