Final answer:
King Charles II gained control of New Netherland by taking advantage of the Anglo-Dutch wars and the English takeover of the Dutch fur trading colony in 1664. He then gave the colony to his brother James, Duke of York, who renamed it New York.
Step-by-step explanation:
King Charles II gained control of New Netherland by taking advantage of the imperial rivalry between the Dutch and the English during the Anglo-Dutch wars.
In 1664, under the threat of an English attack, the Dutch turned control of New Netherland over to the English.
Charles II gave the colony, including present-day New Jersey, to his brother James, Duke of York. The colony was renamed New York in his honor.