Final answer:
Percy Jackson convinced the river gods Hudson and East to stop Kronos's army in 'The Last Olympian' by using his persuasion skills to appeal to their sense of justice, paralleling the negotiation and leadership seen in historical Greek figures.
Step-by-step explanation:
How did Percy convince Hudson and East, river gods, to stop Kronos's army in The Last Olympian? In the narrative of Rick Riordan's Percy Jackson series, specifically in The Last Olympian, Percy Jackson does not convince the river gods Hudson and East using any of the methods mentioned in options 1 through 3. Unlike the Greek heroes Perseus or Achilles, who relied on divine gifts or cunning strategies to accomplish their goals, Percy instead demonstrated exceptional leadership and negotiation skills akin to historical figures like Themistocles who rallied the Athenians to build a navy. Percy's approach most closely resembles Option 4: he used his persuasion skills to appeal to their sense of justice. There is a thematic resonance between Percy's actions and the mythologies and histories of Ancient Greece, where persuasion and valor were instrumental in overcoming great challenges.