You need to drill through the plaster and into the wood framing.
How to hang a wooden sign on wall.
Locate and mark the studs.
Line up the sign and mark for screws before attaching as outlined above.
Hang larger signs with screws through the face.
To the upper cleat attach a 1x1 or 1x2 strip of wood that is 5 1 2 long so that it s flush to the top of the cleat on the artwork.
Do this for both the top and bottom cleats.
Attempting to use fasteners designed for wood or metal walls on a masonry or brick wall will cause the end of the fastener to heat up and dull before it makes an indentation on the material.
Pre drill and countersink pilot holes to avoid splitting the sign.
Use drywall screws to drive through the sign into the wall.
There are a number of different ways to hang the letters up meaning you.
Line up large signs with studs for added security.
How to hang wooden letters on a wall.
Most wall framings set studs every 16 inches so you should be okay to measure from there but double check with a pilot hole.