How do female gymnasts not show their private parts?

if you mean like regular jeans or sweats because the might get in the way of doing skills and they might not stretch far enough

Stretch pants or leggings, or even tights, can get in the way or cause a gymnast to slip. If the gymnast is being spotted doing an advanced skill, the coach could grab the pant leg or the hand could slip, which could cause a dangerous situation. It is NOT for your personal enjoyment.