Capitalize:
* Mount Everest: A specific mountain.
* The Himalayas: A mountain range with a specific name.
* The Rocky Mountains: A mountain range with a specific name.
* Mount Kilimanjaro: A specific mountain.
Don't capitalize:
* a mountain: General reference to a mountain.
* the mountains: General reference to a mountain range.
* the mountain range: General reference to a mountain range.
Key point: If you are referring to a mountain or mountain range with a specific name, capitalize it. If you are using a generic term for mountains, don't capitalize it.