Final answer:
The New Babylonian Empire reached its greatest height during the reign of Nebuchadnezzar II, who made significant architectural contributions to Babylon during the 6th century BCE.
Step-by-step explanation:
The New Babylonian Empire reached its height during the reign of Nebuchadnezzar II. Nebuchadnezzar II reigned in the 6th century BCE and is responsible for rebuilding Babylon into a grand city that featured massive palaces, fortified walls, and the renowned prophylactic "Hanging Gardens". The culmination of the New Babylonian Empire's power and territorial extent was achieved under his rule, making Nebuchadnezzar II the standout figure when talking about the zenith of the Babylonian Empire's prominence.
It is also important to note that the Neo-Babylonian Empire came to an end when Cyrus II of Persia conquered Babylon in 539 BCE, bringing the empire under Persian control. This means that while Nebuchadnezzar II was the apex ruler of the New Babylonian Empire, it was Cyrus II who ultimately conquered the Neo-Babylonians, as mentioned in the provided reference information.