It depends on the airline. Most European airlines defer to ICAO and governmental warnings about flying over Afghanistan and I think Cathay does too.
The prime Great Circle route is up over China, Kyrgyzstan, and Uzbekistan but this would put you to the north of the main Himalayan ranges.
If your flight was on a modified Great Circle (as would be likely to take advantage of winds) and you had crossed part of the Himalayas, it could be the extreme northwest corner of India or even Tajikistan.
BTW, when the 747-400 first entered service on Far Eastern routes there was a major rush to fly over the Himalayas to cut journey times.
A number of very serious turbulence incidents then took place and most airlines stopped flying over the largest peaks, some going back to skirting the area all together.
Does anyone have REAL KNOWLEDGE of the state of play now, as all I ever seem to get on ATC and routes in the area is India's problems with ATC upgrades and the cost of implementation of FANS in the region?