The Ashok Mehta Committee was formed to make recommendations on the issue of the Panchayati Raj System. Panchayati Raj is a system of local self-government in rural areas of India. It empowers the people at the grassroots level by giving them the authority to manage their own local affairs. The committee was tasked with studying the functioning and implementation of the Panchayati Raj system and making recommendations for its improvement.

Option 1, the division of tax revenues between the Centre and States, is not related to the focus of the Ashok Mehta Committee. This issue is typically addressed by other committees or bodies such as the Finance Commission.

Option 3, the appointment of Governors, is also unrelated to the Ashok Mehta Committee. The appointment of Governors falls under the jurisdiction of the President of India and is not within the scope of the committee`s mandate.

Option 4, presidential and vice-presidential elections, is also not the subject of study for the Ashok Mehta Committee. The process of presidential and vice-presidential elections is determined by the Constitution of India and does not require an additional committee`s involvement.

Therefore, the correct answer is option 2, the Panchayati Raj System.