Explanation:

- The Constitution of India provides for a three-tier system of Panchayati Raj for all states with populations exceeding a certain limit.

- Panchayats at the intermediate level are optional for states with a population less than a specified threshold.

- Option 1: Twenty-five lakh - This is not the threshold set by the Constitution for intermediate Panchayats.

- Option 2: Twelve lakh - This limit is too low.

- Option 3: Twenty lakh - The Constitution allows states with a population not exceeding this number to skip constituting Panchayats at the intermediate level.

- Option 4: Fifteen lakh - This is not the correct option based on the constitutional provision.

The correct answer is: Option 3 - twenty lakh.