Option 1: G. K. Gokhale - The correct answer is G. K. Gokhale. Gopal Krishna Gokhale, a prominent Indian social and political leader, was opposed to Annie Besant`s idea of launching the Home Rule Movement. Gokhale believed in a more gradual and moderate approach towards achieving self-rule for India. He believed in education, social reform, and the development of political consciousness among the masses before pursuing more aggressive political actions. Gokhale was a strong advocate for constitutional reforms and worked towards the empowerment of Indians within the British framework. He was also a mentor to Mahatma Gandhi and influenced his political ideologies.

Option 2: Mahatma Gandhi - Mahatma Gandhi was not opposed to Annie Besant`s idea of launching the Home Rule Movement. In fact, Gandhi actively supported the movement and became one of its prominent leaders.

Option 3: Aurobindo Ghosh - Aurobindo Ghosh was not opposed to Annie Besant`s idea of launching the Home Rule Movement. He was a prominent nationalist leader and played an active role in the movement.

Option 4: B. G. Tilak - Bal Gangadhar Tilak was not opposed to Annie Besant