The mountain route used to outflank the Greeks was the Anopaia path, also commonly spelled Anopaea Pass. It ran over the mountains behind the narrow coastal position at Thermopylae and connected the Persian side of the pass with the area behind the Greek defenses.
The route was not a newly discovered secret. Local people knew the trail, which Herodotus describes as a path used in earlier raids against the Phocians. Its importance came from the fact that the main Greek force was positioned to block the road through the narrow pass, while the mountain track allowed an army to approach from the rear.
After Ephialtes showed the route to Xerxes, the Persian commander Hydarnes led troops along it at night. Their movement made the Greek position untenable. Leonidas sent most of the allied army away but retained a rear guard for the final stand. “Anopaea” and “Anopaia” are variant transliterations of the ancient Greek name, so the stored answer identifies the correct route.