Drywall – correct fastener for drywall over plywood

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I'm trying to install mirror brackets into my wall for a lightweight frameless wall mirror (58" x 16").

My attempt at using a hollow wall anchor (Hillman 1/8" DXS drive wall anchor) didn't work very well.
The drywall appears to be 3/8" thick, and directly behind it is some plywood that appears to be fairly thin too.
The anchor just chewed up the drywall leaving a 3/4" diameter hole.

What's the correct fastener to use here?

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Best Answer

Use a molly bolt, sometimes called a toggle bolt. They can be found and any hardware store. The butterfly end opens up on the other side of the wall material. When it is drawn tight it is a very good and strong fastener. While you are at the hardware store pick up a small can of spackel to be used to fill the seen portion of he fastened hole.