Answer: The character speaking in the sentence “I will not let yield, I will not retreat even one inch” is D. the Professor.
Step-by-step explanation: The Professor is the one who says "I will not let yield, I will not retreat even one inch” in Chapter XXXIV from Jules Verne's A Journey to the Center of the Earth. He pronounces these words after the group faces fearful dangers during their sea voyage. In the book, the Professor is the uncle of Axel, the protagonist and narrator of the story. Moreover, throughout the novel, the Professor is depicted as an optimistic man.