Question

how did the spanish justify the forced labor of indigenous peoples under the encomienda system? by offering to share the profits from mining and farming by providing freedom to indigenous peoples after a set number of days by arguing that indigenous peoples were already enslaving each other by claiming they would provide protection and christian instruction

Explanation:

The encomienda system was a labor system in Spanish colonies. The Spanish justified it by claiming they would provide protection (from other potential threats) and Christian instruction (converting Indigenous peoples to Christianity) in return for the labor. This was a common ideological justification used by colonizers to present their exploitation as having a "benevolent" aspect.

Answer:

By claiming they would provide protection and Christian instruction.