The most accurate response regarding the extent and operation of the Inca Empire is: "The Inca Empire extended across the Andes Mountains along the western side of South America."
This statement correctly identifies the geographical location of the Inca Empire, which primarily occupied the Andean region, including present-day Peru and parts of Ecuador, Bolivia, Chile, and Argentina. The other statements either contain inaccuracies or do not accurately reflect the historical context of the Inca Empire.