Specifically, I do not understand how to use the graph on the right. The full datasheet can be found here
The graph on left is showing you power dissipation as a function of load current for different duty cycles; full-on and 50%. The right hand graph is showing you for different thermal resistances (each line) what Tcase_max will be for a given ambient temperature. The datasheet is somewhat ambiguous on how those thermal resistance characteristics were determined, I imagine it depends on the heatsink you use, with 6C/W being no heatsink.