But none of us was there so nobody knows exactly how long it's been that tall.
Even though none of us were there to watch the Himalayas forming, we do understand how they formed. We know that they are very young in relation to other ranges. We also have examples of very old ranges and understand how they formed and subsequently, became worn down.
Since we have a pretty good understanding of the processes on both ends we can say that both processes took far longer than 6000 years. For example, the Appalachians are among the oldest mountains we know of, dating back some 400-500 million years.
Aslan is not a Tame Lion