Plastic anchors like this come packaged with a lot of accessories, but I don't like them for certain types of fixtures. For example, this toilet paper holder right here, if you take a look over here, you'll see what happens. The constant pulling on this causes these to pull right out of the wall.
Now a better choice for a hanging job like this would be something like this threaded anchor. Designed specifically for wallboard, these could often thread right into the holes left by the plastic anchors. You can drive them in by hand as I'm doing or by using a drill and bit driver.
Once the anchor is firmly in place, I reattach the bracket, using pan head screws. Now it's just a matter of slipping the fixture back on the bracket and tightening the set screw.
Well, there you go. If you have plastic anchors that are pulling out of the wall, well, now you know, what to do about it.
