02 Honda Shadow VLX rear cylinder not firing.?

You said that the front fires good but you didn't say if the rear fires good. Plug each wire to a plug(on the rear) and hold it against the block then turn the engine over to see if the plug fires if it does and has a blue spark then its good. open the carb bowl screw to see if there is gas in the left carb. If it has gas then let it drain and then tap the carb with maybe the handle of a screwdriver, float needle valve may be sticking then again let the carb fill with gas.you will have to turn the key on and off a few times to fill the carb as it has a shutoff switch that only operates for a short time if engine isn't running if it still doesn't run then maybe the CDI is the problem because I had a friend that had the same problem and I traced it to the CDI. The CDI can go bad on just 1 cylinder. I also had mine go bad but I was lucky only had to solder the contacts inside the CDI and its been fine for that last 5 years. Honda only makes the bottom half of the CDI and they farm out for the top half to be made so only the top half of the CDI can be repaired,

shoot a little raw gas into the cylinder if it fires [after you put the spark plug back in] then its not getting fuel.

try to start, after that, pull out the sparkplug and look at the color. on google you can find what color of the sparkplug indicates what the problem is.

it maybe not getting fuel or compression.

Maybe its the oil. (Srry, I'm not really a car person. I just answered to earn points.)