We will first mention that no such building was found in the excavations that took place.

If they really existed, they would have been part of the outer walls of Babylon which was considered a botanical wonder.

It is estimated that they were built in 600 BC. and the initiator was Nebuchadnezzar II. It was a gift for his wife.

They were tiered gardens of trees and flowers measuring 122 meters in length and width, and 25 meters in height.

It is considered one of the 7 wonders of the ancient world.

[Source: el.wikipedia.org]