That clicking sound that you hear while your Kawasaki's ZX-6R is running is generated by a loose camshaft timing chain. This chain is driven by the motorcycle's crankshaft, turning the intake and exhaust camshafts at precise intervals to power the motor. The camshaft chain can stretch over time, potentially causing the chain to "jump" off of the camshaft teeth and throw off the motor's delicate timing. To avoid this problem, a spring-loaded tensioner is attached to the motor to keep the chain under constant tension. Occasionally, the tensioner will need to be reset to adjust for chain wear.
Remove the seats from your ZX-6R using the motorcycle's ignition key. Lift the rear seat off of the tail fairing to access the front seat latch. Unlatch the front seat then pull it off of the motorcycle.
Unscrew the fuel tank's mounting bolts near the front fork with a 5-mm Allen wrench. Unscrew the tank's pivot bolt and nut from the frame's seat rails, using a 12-mm socket and a socket wrench. Lift the tank off the motorcycle's frame and unplug the fuel lines. Skip this step if you are working on a 2005 or newer ZX-6R.
Remove the right middle fairing from your ZX-6R, using a 4-mm Allen wrench. Pull the fairing away to access the camshaft chain tensioner on the back of the motor's cylinders.
Unscrew the large bolt from the back of the tensioner's housing with a 14-mm socket and a socket wrench. Pull the bolt's washer and the tensioner rod's spring out of the tensioner housing.
Unscrew the tensioner housing's mounting bolts from you ZX-6R's motor, using a 10-mm socket attached to a socket wrench. Pull the tensioner out of the motor.
Press down on the ratcheting stopper on the end of the tensioner, placed just above the tensioner rod's flat end. Push the rod completely into the tensioner housing and release the ratcheting stopper. Pull the rod out until the stopper clicks 5 times.
Insert the tensioner into the motor, facing the stopper upwards. Screw the tensioner's mounting bolts into place with a 10-mm socket, then tighten the bolts to 97 inch-pounds with a torque wrench.
Slip the tensioner rod's spring into the tensioner housing. Screw the large bolt and its washer into the tensioner housing, using a 14-mm socket. Tighten the bolt to 15 foot-pounds, using a torque wrench.
Reinstall the right middle fairing or fuel tank and both seats, using the reverse method of removal.