Many of the kings of the Greater Mesopotamian region proclaimed themselves to be the “King of Four Quarters”. This term is apparently similar to the Indian term of Cakravartin. A Chakravala Chakravartin is the one who has conquered the four continents. Only Chandragupta Maurya and Ashoka are qualified with this title.
In the Mesopotamia, the Four Quarters referred to Martu in the west, Subartu (or Assur) in the north, Elam in the east and Sumer in the south. Naram-Sin of Akkad, grandson of Sargon of Akkad, was apparently the first to boast of being the King of Four Quarters.
The Akkadian empire, originating in the central Mesopotamia was the first of the great empires. The cause of its destruction was the invasion of Gutians. Gutians belonged to the Zagros mountains somewhere to the North of Elam. The end of Akkadian empire gave rise to the Sumerian or the Ur III empire. Its destruction was caused by the attacks of Amorites from Martu in the west and conquest by the Elamites from the East.
The Amorite dynasty in Babylon reached its peak with Hammurabi. Apparently forgetting his heritage, Hammurabi destroyed Mari, the great city of the Amorites. Defeating the Elamites in the west, the Larsans in the south, the Amorites of Mari in the east and Eashunna in the north, he became the King of Four Quarters. Whether he defeated the Assyrians is unclear to me at the moment.
Below are some of the maps that have helped me understand the locations of the various cities and kingdoms. All of them are sourced from Wiki. The links to the original wiki page is also given for attribution.