Power off the mower and remove the keys. Open the front hood over the engine and wait for the engine to cool before proceeding.
Find the motor's flywheel. The circular, covered flywheel will be on the top of the back area of the Kohler 12-HP engine. The cover over the flywheel is iron and is held in place with bolts. Remove the bolts using a socket wrench, pull off the cover and set it aside.
Remove the Kohler 12-HP motor's flywheel, using a flywheel pulley tool. Place the pulley over and onto the flywheel, and use the wrench to tighten the pulley's bolt until the flywheel comes free from the motor. The removal of the flywheel provides partial access to the motor's PTO shaft.
Remove the bolts from the rectangular oil pan at the bottom of the motor, using the socket wrench. The oil pan's removal provides further access to the PTO shaft, which is now visible.
Remove the bolts along the PTO shaft that secure it to the Kohler 12-HP motor, using the socket wrench.
Hit the Kohler 12-HP motor with a rubber mallet at the center of the engine, just below where you removed the flywheel. This will free the PTO shaft from the motor.