Is there perhaps an image of the passage or you can type it out in order for us to help you? :3
Answer: By leading the Utilitarian movement.
Explanation: John Stuart Mill is an English phylosopher,known as one the greatest English phylosophers in history,he was born the year 1806. He was the one who led the Utilitarian movement which is known to be a movement concerned about the happiness of the people.
The Utilitarian Theory tries to show that all happiness is very vital for the wellbeing of man,and that all Government actions should be geared towards completly removing pains from the lives of people.
Persuade means to convince someone to believe, follow, accept, etc. your idea or suggestion. So your answer should be C. To Convince. Hope this helps! =^-^=