Option 1: 3rd September, 1946 - This date is not the correct answer. It was not declared as the Direct Action Day by the Muslim League.

Option 2: 16th August, 1946 - This is the correct answer. The Muslim League declared 16th August, 1946, as the Direct Action Day. On this day, violent protests and riots took place in Kolkata (formerly known as Calcutta), resulting in many casualties.

Option 3: 16th May, 1946 - This date is not the correct answer. It does not correspond to the day the Muslim League declared as the Direct Action Day.

Option 4: 4th December, 1946 - This date is not the correct answer. It does not correspond to the day the Muslim League declared as the Direct Action Day.

Overall, option 2, 16th August, 1946, is the correct answer as it aligns with the historical event of the Muslim League declaring it as the Direct Action Day.