Put a non-skid rug pad under it.
If over carpet-not much. Rugs don't like to be on another rug. Actually will harm/ruin both the carpet and area rug. If you want that look need to put down a solid surface floor so a non skid pad will work.
Add some silicone sealer to the edges underneath. Once dry the rug will stop sliding up.
Hi Sharon. I'm Cindy. Two way tape will keep your rug in place.
even on carpet?
It looks like your rug was stored folded instead of rolled. Try folding it the opposite direction for a while or use a steam iron to relax the bend.
Double sided tape or underpad will help
Hand tack (loosely sew) a long strip of Velcro (use the rough side) to one end of the rug. It should stick to the carpet underneath. It does on mine. Just make sure you put it on the tail edge of the top rug, otherwise it will bunch up on itself.
Be careful about two way tape. I used it on the back of my rug and it left sticky residue on my carpet when I removed the rug. I had the rug down on the carpet for several years. I have had to work really hard to remove the residue.