Question

great technical facility on an instrument is called

Answer 1

Technical facility would mean in music the ability to play your instrument, physically.

Technique is the collection of things that you do to physically move your instrument, to make it make sound. It includes; posture, proper motion, proper breathing, and the practice of moving your hands/fingers/lips etc. in the proper way.

Think of playing an instrument as being the combination of two things, theory and technique.
Theory is the mental game,
Technique is the physical game.

Facility in this instance means ease.