Considering the type of terrain they frequent, a flat tire now and then is to be expected on a garden tractor. Flats are not difficult to fix. It is only when the hole or gash is large, and occurs in the sidewall, that the tire needs replacing, not repairing. You can fix a flat tire on your garden tractor with little difficulty, and usually quite quickly.
Fill a spray bottle halfway with water. Add 3 tablespoons of dish detergent.
Inflate the flat tire five pounds beyond the recommended PSI. Starting at the top of the tire, liberally spray the soapy water over the tire's surface. Wait a moment, then look for the appearance of bubbles in the area you just sprayed. Continue spraying the tire, section by section, and looking for bubbles.
Use the white crayon to mark the area that is leaking, as indicated by the bubbles. If the object that caused the leak is visible, grasp it with needle nose pliers and remove it.
Use the rasp tool from the tire plug kit and insert it into the hole. Using a sawing motion, move the tool back and forth about six times. Remove the tool.
Pull a tire plug strip free from the kit. Using the insertion tool from the kit, thread the plug strip through the tool's needle eye until there are equal amounts of the strip on either side.
Apply three or four drops of rubber cement, included with the kit, to the very tip of the insertion tool, and with firm pressure, insert the plug strip into the hole until 1/2 inch of the strip remains outside of the tire.
Twist the insertion tool a half turn, and then remove it with a sharp tug. Clip the remaining plug strip to 1/4 inch in length.
Inflate the tire, and spray the soapy water on the repaired area. Check for bubbles. If bubbles appear, repeat the procedure with a new plug.