Make sure the Troy-Bilt riding lawn mower model 31C707 has gas in the gas tank.
Remove the keys from the Troy-Bilt riding mower's ignition if the engine is cranking but is not starting. Open the hood of the mower and look inside to find the spark plug and the attached black plug wire. Ensure the plug wire is not loose from the plug -- if it is, reinsert and secure it. If the plug wire is not loose, disconnect it from the existing spark plug and reinsert it into a new spark plug.
Open the mower's front hood again and follow the trail of the black plug wire to the distinctly circular magnetic coil near the back of the assembly. Notice the part directly behind the magnetic coil. This is the Troy-Bilt's flywheel. The slight space between both these parts is the air gap. This air gap is supposed to be precisely between 0.010 and 0.015 of an inch in size. Measure the air gap to check.
Reposition the magnetic coil in relation to the flywheel as necessary if the measurement proves to lie outside the recommended gap size. Loosen the coil with a wrench and then apply light pressure to move it closer or further away from the flywheel in order to resize the air gap.
Close the Troy-Bilt riding mower's hood and test the engine.