Mahatma Gandhi made his first public appearance in India after returning from South Africa at the Banaras Hindu University in 1916. This event marked his reintroduction into the Indian political scene and the beginning of his role as a leader in the Indian independence movement.

Option 1, Champaran in 1917, is incorrect because his first public appearance did not take place in Champaran. However, Gandhi did play a significant role in the Champaran Satyagraha in 1917, where he advocated for the rights of indigo farmers.

Option 2, Lucknow in 1919, is also incorrect. Mahatma Gandhi did visit Lucknow in 1919, but it was not his first public appearance in India after returning from South Africa.

Option 4, Ahmedabad in 1918, is also incorrect. Gandhi did visit Ahmedabad in 1918 but it was not his first public appearance in India.

In summary, Mahatma Gandhi`s first public appearance in India after coming back from South Africa was at the Banaras Hindu University in 1916.