Final answer:
The question about how Peter talked the Turks into letting him go is a bit vague without specific historical context. If it refers to Shah Abbas' dealings with the Ottomans, he gave up substantial territories in a peace treaty. Additionally, peaceful acquisition of territories in historical contexts included paying tribute, while in New Amsterdam's case, it involved a surrender due to logistical shortcomings.
Step-by-step explanation:
Regarding the question of how Peter talked the Turks into letting him go, the correct answer from the provided options is not listed. However, looking at historical context, Shah Abbas of Iran, who was contemporaneous with the period in question, did have to negotiate with the Ottomans by signing a peace treaty in 1590 which resulted in giving up nearly half of his territory to them.
When it comes to methods used by ancient empires to acquire territory, peaceful means included options such as tribute, which could be seen during the Ottoman Empire's expansion, where they often made conquered cities pay tribute while keeping their own administration. Peter Stuyvesant, in contrast, surrendered New Amsterdam to the English because the Dutch were under-provisioned and the colonists preferred to ensure the safety of their property over resisting English rule.