which empire accomplishments include the ishtar gate, the hanging gardens of babylon, and knowledge of astronomy and medicine

The correct answer is - The Babylonian Empire.

The Babylonian Empire was one of the most advanced empires in the world and it was the birthplace of lots of inventions, as well as setting the foundations for some of the sciences, but they were also known for their creativity and sense for aesthetics, and beautiful architecture. This civilization was located between and in close proximity of the Tigris and Euphrates rivers, in the Middle East, on the territory of the modern day country of Iraq.

It's the Chaldean empire