The Quit India Movement was launched in 1942 in the month of August.

Option 1 (January) is incorrect because the Quit India Movement did not begin in January.

Option 2 (March) is incorrect because the Quit India Movement did not begin in March.

Option 3 (August) is correct. The Quit India Movement, also known as the August Movement, was launched on August 8, 1942, by Mahatma Gandhi in response to the British government`s refusal to grant India immediate independence. The movement aimed to demand the complete withdrawal of the British from India.

Option 4 (December) is incorrect because the Quit India Movement did not begin in December.

Therefore, the correct answer is option 3 (August).