Before doing the tests suggested, I would make sure that the battery is fully charged, connections are clean and tight, and the solenoid is grounded. You might end up replacing parts when you don’t have to.
Hook a small 12 volt light across the two big terminals on the solenoid, should be lit. Turn the key switch to start, light should go out. If not the solenoid is bad, if it does go out the starter is bad or the cable to the starter is bad. Hook the light to the starter terminal if you can access it and a grounding point , should light up when you turn the key switch to start. Bad starter if so.
Used test light as suggested on 2 big terminals of solenoid and no light. Also used test light on starter and this lights up when I turn ignition key.Probably not a Honda engine, Should be a Kohler courage, unless it was re powered.
as rivets said, make sure the battery is charged and all grounds and connections are clean and tight.