They "traded" it at gunpoint, as was the custom at the time. That is to say, the English captured it, and a decade later after the Third Anglo-Dutch war the Dutch decided they didn't want it back (it wasn't a very profitable colony), so in the Treaty of Westminster they got Suriname instead.

I've written a bit about the Dutch WIC and VOC, in particular relative to Spain and Portugal that gives context of Dutch interest in the Americas and in East Indies.

More to the point, which era/year are you referring to specifically? The Dutch lost control of New Amsterdam to the English in 1664, while the two countries were theoretically at peace with each other. The second Anglo-Dutch war started very soon after. At the conclusion of this war, the Dutch preferred to strengthen their hold in the east Indies spice trade, and to re-gain access to English markets that they had been barred from previously. The cost of this settlement was that New Amsterdam, already controlled by England, be ceded to England.