Final answer:
The Neo-Babylonians made Judah and Jerusalem to rejoice over their enemies by conquering the city and destroying it in 586 BCE. The captivity ended when the Persian king Cyrus the Great permitted the Judeans to return and rebuild the temple.
Step-by-step explanation:
In the context of the destruction and captivity of Jerusalem, it was the Neo-Babylonians who made Judah and Jerusalem to rejoice over their enemies. The Neo-Babylonians conquered Jerusalem and destroyed the city and its temple in 586 BCE. This event is known as the Babylonian Captivity of the Jews. The captivity ended when the Persian king Cyrus the Great allowed the unassimilated Judeans to return to Judah and rebuild the temple.