The “rough riders” were
a cuban revolutionaries who battled the spanish for independence.
b. a volunteer cavalry unit in the spanish-american war.
c. newspaper owners who influenced public opinion by exaggerating the truth.
d. spanish generals in cuba who mistreated the civilian population.

The Rough riders were actually fighting FOR The US, not for any other country, so we can exclude all the answer that mention other countries' fighters. We are left with:

B. a volunteer cavalry unit in the Spanish-American War.
C. newspaper owners who influenced public opinion by exaggerating the truth.

the truth is the frist option, 

B. a volunteer cavalry unit in the Spanish-American War. Actually only one group of such volunteers was given this name, specifically the first unit. The army was a volunteer army because the US did not have sufficient funds to properly fund an army at that time. 

4. great depression