Just a general arm chair opinion:
The spark plug cylinder on the left in the picture is the suspect cylinder when doing a compression or leakdown COMPARISON test. Comparing the left oily/carbon/fouled spark plug cylinder to the right plug's cylinder.
The right plug is worn out but no need in throwing good money at bad replacing such right now.
If the left plug's cylinder compression is 15-20lbs or more lower than the right plug cylinder then head gasket is suspect. (or the rings on that cylinder) If both cylinder have about same compression (within 5 pounds the rings on both are suspect.
I prefer to do a leak down test but doing a leak down is not as user friendly as the compression test. (you might could rent a leak down tester if you have a air compressor) You can review on-line the procedure for doing small engine leak down tests.
On that Briggs twin another thing I would visually look at is the breather hose that plugs into the back of the air breather intake. I've seen people accidently leave that hose disconnected from the plastic breather intake and the engine will suck dust straight into the air intake via way of the dime sized hole into the carb's throat and the rings will go fast. This hole bypasses the air filter.
The spark plug cylinder on the left in the picture is the suspect cylinder when doing a compression or leakdown COMPARISON test. Comparing the left oily/carbon/fouled spark plug cylinder to the right plug's cylinder.
The right plug is worn out but no need in throwing good money at bad replacing such right now.
If the left plug's cylinder compression is 15-20lbs or more lower than the right plug cylinder then head gasket is suspect. (or the rings on that cylinder) If both cylinder have about same compression (within 5 pounds the rings on both are suspect.
I prefer to do a leak down test but doing a leak down is not as user friendly as the compression test. (you might could rent a leak down tester if you have a air compressor) You can review on-line the procedure for doing small engine leak down tests.
On that Briggs twin another thing I would visually look at is the breather hose that plugs into the back of the air breather intake. I've seen people accidently leave that hose disconnected from the plastic breather intake and the engine will suck dust straight into the air intake via way of the dime sized hole into the carb's throat and the rings will go fast. This hole bypasses the air filter.