Final answer:
The Spanish government maintained control over its American colonies through political organization into viceroyalties, converting natives to Christianity, teaching them Spanish culture, a system of castas, and the strategic design of towns; hence, the comprehensive answer is '6) all of the above'.
Step-by-step explanation:
The Spanish government maintained control over its American colonies through a combination of methods. Political organization into viceroyalties was essential for governance, as appointed viceroys, judges, governors, and mayors executed laws and regulations made by the Council of the Indies.
Converting Indians to Christianity was a key strategy for cultural integration and control, as the Crown sought to civilize and dominate through religious conversion. Moreover, teaching Indians Spanish culture was part of the broader goal of assimilating native populations and establishing Spanish societal norms.
Social hierarchy was reinforced through the establishment of castas, a system that organized individuals based on racial and social status. The physical design and arrangement of Spanish towns, including their central plazas and grid-pattern streets, reflected the Crown's intention for administrative efficiency and control. Therefore, the answer to how the Spanish government maintained such control over its American colonies is '6) all of the above'.