Lay the 2-by-2-by-36-inch board flat on a work surface. Measure from one end of the board using a tape measure and mark the board at 2, 6, 18, 30 and 34 inches with a pencil. This is the back for the towel rack.
Adjust the fence on a drill press to drill the center of a 2-inch wide board. Insert a 1-inch drill bit into the drill. A drill press has an adjustable back called a fence. Loosen the knobs on the fence and slide it along the table or flat surface on the drill press until it is aligned to drill a hole 1 inch from the front side of the fence. Tighten the turn knobs once you have it positioned in the correct location on the table of the drill press.
Place the back flat on the table of the drill press with the pencil measurement marks facing up. Drill a 1-inch diameter hole all the way through the back at the 6-, 18- and 30-inch pencil marks with the drill press. These are the holes for the dowels.
Remove the 1-inch drill bit from the drill press and insert a 1/4-inch drill bit. Rotate the 2-by-2-by-34-inch board so that the 1-inch diameter holes are on the sides of the board and the un-drilled side is facing up. Drill a 1/4-inch diameter hole through the 2- and 34-inch pencil measurement marks with the drill press. These are the mounting holes for the towel racks.
Apply wood glue to inside of the 1-inch diameter holes using a cotton swab. Slide the 1-inch diameter dowels through the holes in the back so that 13-inches of the dowel extends from each side of the back board. The dowels are oriented horizontally on the wall and run parallel to the wall. You can hang three towels on each side of the back board, one on each of the three 13-inch sections of dowel that extend from each side of the board.
Wipe off any excess glue that oozes out from around the dowels with a damp cloth. Allow the glue to dry 24 hours before handling it.
Spray an even coat of lacquer onto the towel rack assembly. Allow the lacquer to dry for at least four hours and apply a second coat. Wait 24 hours before mounting the towel rack.