The correct answer to this open question is the following.
The roles and responsibilities of the counties in New Mexico are the following.
Counties in the state of New Mexico are ruled by a board of commissioners elected by the citizens. New Mexico has 33 counties whose responsibilities are the administration and operation of the country, its, people, resources, and the enforcement of the law. For that to happen, each country has -besides the commissioners- a treasurer, assistance, a sheriff, and a judge.
Among the most important counties in New Mexico, we find Colfax, Cibola, Guadalupe, Bernalillo, Rio Arriba, Mora, and Luna county.