The correct interpretation of the image concerning 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 accurately describes the geographic span of the Inca Empire, which was primarily located in the Andean region, encompassing parts of present-day Peru, Bolivia, Ecuador, and extending into Chile and Argentina. The other statements provide inaccurate or misleading characterizations of the Empire's geographical and operational aspects.