Question

The capital of a great empire that included much of Mesopotamia was: Memphis Sumer Hammurabi Babylon

Answer 1

Babylon. 
It's asking for the capital of the Babylonian Empire, which was Babylon.

Memphis was in Egypt (and there's a newer one in Tennessee that has significantly fewer pyramids), Sumer was the name of a Mesopotamian civilization that became Babylonians, Hammurabi was a King of Babylon who wrote down his laws on a rock, which we found and were impressed with, because its the oldest such thing we've ever found.