In a sense, not much happens in this episode. Covering a bit over a century, the borders of Babylon are going to remain more or less stable for most of this episode, and the people are going to enjoy a century of generalized quiet prosperity. Covering the later successors of Hammurabi, Abi-Eshuh, Ammi-Ditana, Ammi-Saduqa, and Samsu-Ditana, we will see scientific and legal advances, good government, and also the quite sudden and total destruction of Babylon, both city and empire.
I am, in all of my discussions of succession today, assuming that each new king is the son of the previous king. Given the extremely long reigns of each monarch, this is almost certainly not the case in at least one or two of them, and at some point a son must surely have been passed over for a grandson. However, it isn't clear which of the kings was a grandson of their predicessor and which was a son, so for simplicity I am just going with son for each, which is what seems to be the standard assumption for lack of other evidence. In private though, I would make the possibly baseless guess that it was Ammi-Ditana who was an extra generation removed.