Final answer:
The correct answer is a. The man responsible for finding paths for John C. Fremont and after whom Nevada's capital is named is Kit Carson, a key figure in the westward expansion of the United States.
Step-by-step explanation:
The man who found paths for John C. Fremont and for whom Nevada's capital is named after is Kit Carson. Carson was a frontiersman and guide who played a significant role in the westward expansion of the United States. Although Meriwether Lewis and William Clark are well-known for their expedition to explore the Louisiana Purchase and the western portion of the United States, Kit Carson is the individual most closely associated with the discovery of routes through the western territories and leading John C. Fremont on his expeditions.
Nevada's capital, Carson City, is indeed named after Kit Carson, acknowledging his contributions to the exploration and settlement of the American West.