The correct answer is option 3: "Buddha or Karl Marx".

Let`s analyze each option to understand why it is correct or incorrect:

Option 1: "The Discovery of India" is a book written by Jawaharlal Nehru, not B. R. Ambedkar. Therefore, this option is incorrect.

Option 2: "My Life" is an autobiography written by Mahatma Gandhi, not B. R. Ambedkar. So, this option is also incorrect.

Option 3: "Buddha or Karl Marx" is a book written by B. R. Ambedkar, a prominent figure in India`s social and political history. The book delves into the comparison of the teachings of Buddha and Karl Marx and their relevance to the liberation of the oppressed. This is the correct option.

Option 4: "Hind Swaraj" is a book written by Mahatma Gandhi, not B. R. Ambedkar. Thus, this option is incorrect.

To summarize, out of the given options, B. R. Ambedkar wrote the book "Buddha or Karl Marx" (option 3).