It seems to be that the main idea of this passage is that even with the would full of doubt, King won't give up the fight. This would be option D.
Lets take this passage and compare it to the options.
"I refuse to accept despair as the final response to ambiguities of history."
A. Violence should only be used as a last resort to end oppression. No where in this passage does it mention violence.
B. Seeing all the violence makes King feel uncertain about the future. Again, no violence.
C. Depression is the only option when faced with unending violence. Although this might look correct to some, here is he is giving up. Luther says, "I refuse to accept despair."
D. Even though the world is full of doubt, King won't give up the fight. Ding Ding!! "I refuse to accept despair as the final response to ambiguities of history." Or "I will not give up, no matter how full of doubt the world is." We can see here he is not giving up even when everyone is doubting them.
I hope you understand! Have a great day! :)
