Being short in stature I have always found it difficult to be high enough standing over any table to be able to assemble large hoops with fabric/stabilizer etc without having everything shift and move out of alignment. Very early on in my embroidering addiction journey I began using masking tape/painter's tape to help me do this.
I use masking tap on two of the the under sides of the inner hoop that sits on top of the fabric to be embroidered. I just tear off lengths of tape long enough to cover two of the sides, fold it in half and stick one side to the hoop as shown.
When the hoop is flipped over the half side of tape not stuck to the hoop sticks to the fabric to be hooped and does not move as you insert the inner hoop into the outer hoop. I still use this method everytime I hoop with my larger hoops especially the ones that are larger than 8 inches in length.
You can also stop the outer hoop from moving around by placing it against a solid board such as a chopping board. If you have a hoop that is completely rectangular or square without being rounded on the top and bottom you can tack some pieces of wooden beading onto a board base to stop the outer hoop from moving around.
I know there are specialised accessories to help us hoop but I have always achieved fairly accurate success with my own home grown ideas.