lawn mower how to stop carbon build up on spark plug?

Carbon usually comes from partially burned or unburned fuel. Meaning your carburetor is running too rich. Does the engine exhaust also look black? That is the sign of rich engine. Blue or white is oil burning. After sitting for the winter, if you are just beginning to use it for the season drain out all the old gas and put in good quality gas like Chevron or Shell and use premium. It may loosen the sticking parts in the carburetor. There are also some fuel conditioning additives that may help the carburetor.

Lawn Mower Spark Plug

Before you consider an overhaul or a new mower, buy a one number hotter plug, and try that. Some times the spark gets weak on a plug and a newer just slightly hotter running plug will keep it clean longer. Don't go too hot or you'll melt the top of the piston.

Is the engine burning a bit of oil? If not you should clean and rebuild the carburetor. If it is burning oil there isn't much you can do, to fix it would probably cost more than replacing the mower. If it is burning oil you could try changing the oil and putting a little oil additive in it like STP. Might get a bit more life out of it.

The engine needs to go to a certified mechanic for an overhaul. It might make more sense just to replace the mower. Compare costs and base your decision on that.

Its running to rich