Yamaha banshee will not start

Question edited for FULL 'make model (what it is)', from 'banshee'.
Question moved from Motorcycles to correct Category.

Check spark plugs.
Clean Carb.
Check timing.

More here, it is a known issue.

https://www.google.com/search?q=Yamaha+banshee+atv+backfires

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14 - 41 = 2.93 ratio
15 - 46 = 3.06 ratio..
6-7 links.. you need to move the axle all the way forward when installing a new chain... (it will stretch!) moving the axle all the way forward gives you plenty of adjustment later!!

It looks like your compression is too low (worn rings from dusted motor) Push starting spins the motor faster than kick starting and when hot the rings expand just enough to seal off. Before kicking a cold motor try putting in a squirt or two of engine oil in the plug hole to see if there is a difference.

check your pickup coil?

Check the plug color to see if it is normal. I would put new spark plug caps and new spark plugs on the machine and see if that helps . From what you describe , if the spark plug caps do not work , you will probably have to either , adjust your air screw setting or change your pilot jets up one size to compensate for the other changes.

Could be air block in the petrol tube and clean the carborator and remove the dust and dirt to run the unit. Cleran the petrol tank atleast once in a year to avoid dust formation at the bottom of the fuel tank. Adjust the gap in the spark plug to standard specification to avoid back fireing.

Carburetor on the side that's wet, need repair.