Affix the broken piece if the piece is still attached to the particle board then dry fit it first to determine how well it will sit.
Fix cabinet door hinge particle board epoxy.
Then glue the wood dowel in cut it off flush and once dried drill your new hole for the hardware again in the new wooden dowel.
And it will hold for a long time.
Transfer a small amount of polyester resin auto body filler or epoxy wood filler to a flat surface.
Mix it with hardener in the manufacturer s recommended proportion.
Then fill the glue injector with the wood glue and apply it where the piece broke off as well as on the piece itself.
Taking a couple of wooden tooth picks in hand dip them in the bondo.
Now insert them into the over sized hole that is too large for the cabinet door screw.
Wait several minutes for the wood glue to get tacky and press the piece in place.
You drill the striped screw hole out to allow a properly size wood dowel to be inserted.
Use wooden toothpicks to fill.
Step 4 fill the hole in with the epoxy putty.
Continue to fill the hole with toothpicks and the filler until nothing else will fit into the hole.
1 mix the two part epoxy filler thoroughly together.