To answer this question, the user needs to know who Mahatma Hansraj is and basic knowledge about his life.

Mahatma Hansraj was an Indian educationist who founded the Dayanand Anglo-Vedic (DAV) school system. He was born in Punjab, India, and is known for his efforts to promote education in India.

Now, let's go through each option and determine which one is correct:

A. April 6th 1894: This option is incorrect as it is not the birth date of Mahatma Hansraj.

B. Sept. 21st 1885: This option is incorrect as it is not the birth date of Mahatma Hansraj.

C. Sept. 21st 1870: This option is incorrect as it is not the birth date of Mahatma Hansraj.

D. April 14th 1864: This option is correct. Mahatma Hansraj was born on April 14th, 1864, in Punjab, India.

Therefore, the answer is: D