6.75 Hp means nothing apart from the fact you are literate enough to read the sticker on the mower.
If you want good information that might be specific to your engine we need the model & code number.
Some general information which may or may not apply to your engine because we have no idea which of the 256 6,75Hp B &S engines you have.
Buy a neon tube in line spark tester and install it where you can see it easily.
Buy a can of starter fluid.
Start the mower and watch the tester.
If the spark stops before the engine you have an electrical problem
Disconnect the single thin wire that goes to the coil and try again.
Engine continues to run they your problem is in the mower wiring.
Engine stops the module is cactus and needs replacing.
Engine stops before the spark, you have a fuel problem.
Start the engine and spray short bursts of starter fluid down the carb.
If you can keep it running for a minute or so then you have a fuel supply problem.
If you get a lot of continious black smoke you have too much fuel.
