Final answer:
James Oglethorpe gained the friendship of Georgia Yamacraw Indians by helping them defend their land against enemies.
Step-by-step explanation:
To gain the friendship of the Georgia Yamacraw Indians, James Oglethorpe helped them defend their land against enemies. He established a militia force in the Georgia colony composed of small farmers, merchants, and artisans who would protect both the colonists and the Yamacraw Indians from Spanish and Indian attacks. Oglethorpe's efforts to defend the Yamacraw Indians and their land helped foster a positive relationship and friendship between them.