Inside out means with the inner surface turned to the outside. Your jumper is inside out, turn it inside out, wear it inside out.
It also means thoroughly, so knowing something inside out is knowing every part of it, and that sense is a shortening of inside and out. Washing dark clothes inside out keeps the colour.
1phraseinside outWith the inner surface turned to the outside.
“He was in such a hurry that he put his T-shirt on inside out.”
inside out is a position.
In the thorough sense it is a shortening of inside and out.
In the sense thoroughly, an asyndetic a clipping of inside and out.
Etymology from Wiktionary, CC BY-SA