Okay. So here is more progress.
Here is how I attach blocking to cabinet sides.
Equipment
I forgot to include paper towels.
Slather glue on the block and in the groove.
Use you finger to make sure the glue completely covers the block. Don't be afraid to get dirty.
Use a nail gun to clamp the block to the cabinet side. The nails are just to clamp the block in place until the glue dries. The glue is the strength of the joint.
Wipe off excess glue with lots of paper towels.
Don't forget to wipe down your tip before you put it away.
Dispose of the evidence. Have a drink. Pfft. Looks like a Friday night.