Best thing you can do is spend the $ 49 and buy the JD technical manual for your mower
That will turn you into an expert over night , depending upon how fast you can read .
Remove the blower housing and remove the kill wires ( thin one ) from each magneto coil .
Start the engine
Problem goes away = bad wiring
Problem stays = fuel or valve problem
Remove both the rocker covers
rotate the engine by turning the flywheel by hand
The heads are left right mirrors of each other
So the bad one should do exactly the same things as he good one, just at a different time and the positions of the valves & rockers should be the same.
Take valve cover off dead side and see if push rods are still in place, go on youtube and type in how to adjust valves on Briggs and Stratten, if push rods are off you need to pull them out and make sure not damaged, put on flat surface and roll to see if out of round (if so replace) make sure you see which push rod goes where they need to go back in same spot, if in place adjust both cylinders valves, if still dead take out spark plugs on both sides put your thumb over dead cylinder spark plug hole spin engine with starter it should blow your thumb off if it doesn't you have a deeper problem. tell us what you find.