Correct option is B
The correct answer is: (b) latter
Later – comparative form of "late," generally used when comparing two times or events, but not ideal in this context.
Latter – refers to the second of two parts or items previously mentioned or implied, and is often used with expressions like "the latter half."
Late – usually refers to something that happened in the past or someone who has died, not suitable here.
Lateness – noun form, refers to being late, incorrect in this sentence.
So, the complete sentence is:
My research focuses on the latter half of the eighteenth century.