My john deere 345 series mower is backfiring and won't start. I recently had the heads off replacing the gaskets and when I got it back together it won't crank. I think the valve timing isn't right. Does anyone know how to time the valves on this mower?

Hi,
Yes, I do. Depending on the age of the machine, You have an 18HP or 20HP water-cooled Kawasaki FDxxxV engine. The "xxx's" transpose to the displacement as that is the main difference in the HP ratings.
Remove the hood by unplugging the light harness and either swing forward to just before fully open and it will unlatch from the brackets on either side with a small movement; or if an original it will have two sleeves secured by hairpins on pins on either side. Another hole should be visible inward on the same pins and you move the hairpins to those holes and slip the sleeves inward.
This done, you will have direct access to the valve covers. Remove the four bolts holding them in place with a 10mm socket to teveal the rocker arms. Loosen the adjustment with a 9mm wrench and small adjustable to take the tension of the pushrods. Remove the pushrods and inspect for straightness. No wobble or bow should be visible. If there is, they have to be replaced. Very old engines had a composite cam gear that could disintegate and cause your symptoms, though most should have faied long ago.
At any rate, remove the plugs so that you can spin the engine by hand. With the locking nuts and adjusting screws on the rocker arms backed of and the engine tirned to bring the piston to the top on one side; try to fit the pushrods in place on that side. I they do not seem to fit, turn the engine exactly one revolution and try again. It will probably require a flashlight shined into the block to see the recesses in the tappets where the pushrods seat. Once the pushrods are in on one side, thread the adjustment screw down snug to hold them in place. Repeat on other side to secure all pushrods. I use a dowel or something inserted through the spark plug holes to judge the piston location; and do not be surprised if this takes a number of turns of the engine.
Well, stuffs in place! Now to adjust! First turn the engine over several time by hand to observe the movement of the rocker arms. Then bring one side to TDC on compression and adjust to a snug 0.006" on both valves and carefully lock them with the nut. Do not be afraid to repeat until you are satified with the adjustment; and repeat on the other side by bringing the piston into position on that side.
I usually will turn the engine over many times by hand during this operation. It is now time to put the cover back on with the four shoulder screws for each. Before you do, inspect the shaped square o-ring that is the gasket; if damaged, you will have an oil leak. If all is fine, then put the covers on. It does NOT take a lot of tightening, just good and snug.
Now would be a time to try to start the engine. If it does, replace the hood. Not not post again.
A side note is that this engine "hates" dirty air filters and will foul a plug in a heartbeat!
Peace,
Clarke