Final answer:
The Viceroyalty of Brazil was not one of the viceroyalties established by Spain in the Americas, making it the correct answer; Brazil was a Portuguese colony.
Step-by-step explanation:
The student asked which of the following was not one of the five viceroyalties established in the Americas: the Viceroyalty of New Spain, the Viceroyalty of Peru, the Viceroyalty of Brazil, or the Viceroyalty of New Granada.
Based on the historical data, the Viceroyalty of Brazil is not one of the four viceroyalties since the territory known as Brazil was a Portuguese colony, not a Spanish one.
The Spanish Crown established four main viceroyalties in the Americas: the Viceroyalty of New Spain, with its capital at Mexico City; the Viceroyalty of Peru, with its capital at Lima; the Viceroyalty of New Granada, with its capital at Bogota; and the Viceroyalty of the Río de la Plata, with its capital at Buenos Aires.
Each one of these viceroyalties played an essential role during the colonial period under the Spanish rule, different from the Portuguese administration of Brazil.