When using a toggle bolt, the bolt must be run through the item to be attached.
From the stltoday.com
If the installation has to be placed in a section of wall with no stud available, use a toggle bolt.
From the dailyherald.com
A toggle bolt has a spring-loaded flange that spreads like wings and attaches to the rear of a finished wall.
From the sfgate.com
The hole should be just big enough to get the collapsed spring-loaded wing of the toggle bolt through each hole.
From the sfgate.com
One is a toggle bolt.
From the stltoday.com
The toggle bolt works in a similar way but usually requires a larger hole, which you might have if you've tried some of these other options and failed by this point.