Step 1: Understanding the Concept:
The question requires arranging four of the six major Tabla Gharanas chronologically based on their establishment. This pertains to the history and evolution of Tabla playing.
Step 2: Detailed Explanation:
The generally accepted chronological development of these gharanas is as follows:
1. (C) Lucknow Gharana: Recognized as the oldest among the 'Purbi Baaj' gharanas, established in the late 18th century by Miyan Bakshu Khan and Modhu Khan.
2. (B) Farukhabad Gharana: Founded by Haji Vilayat Ali Khan, a disciple of Miyan Bakshu Khan of Lucknow, hence established subsequent to the Lucknow Gharana.
3. (D) Punjab Gharana: Developed independently, its codification as a significant gharana is generally dated to the early 19th century under Miyan Qader Baksh II.
4. (A) Banaras Gharana: Established by Pandit Ram Sahai in the early 19th century. He was a disciple of Modhu Khan from Lucknow. Although its origins are contemporaneous with the Farukhabad and Punjab gharanas, many chronologies place it after them.
Considering the provided options, the sequence (C) Lucknow $\rightarrow$ (B) Farukhabad $\rightarrow$ (D) Punjab $\rightarrow$ (A) Banaras presents a historically consistent ordering.
Step 3: Final Answer:
The correct chronological order is Lucknow, Farukhabad, Punjab, and Banaras.