The statement that best analyzes how events that led to the fall of the Roman Empire and the Han Dynasty supported Franklin’s statement is:
Both were invaded by nomadic groups who first attacked regions farthest away from the seats of government.
This response directly relates to Franklin's metaphor about the edges of an empire being the most vulnerable. In both cases, invasions often started at the periphery before affecting the core of the empire, illustrating how the “cake” of the empire could be diminished from the outside.