How to adjust the valves on a Kohler command 13 engine on a Husqvarna

The valves do have adjustment. Details in the link.

https://www.google.com/search?q=kohler+25+hp+valve+adjustment

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You have the wire from the starter switch that activates the solenoid on the wrong side of the solenoid. Switch the 2 wires side for side.

not important, what's important is that they are absolutely clean, including the four brass high speed jets located in the bottom center portion of the carburetor.

That model engine's carburetors has fixed jets, BUT if the slow speed jets are adjustable, earlier model carburetors have been installed. If so...................

The four adjustable needle valves control the flow of fuel in relation to the set air flow, adjusted as follows (if needed).

(Dual Carb V/4 With 4 (2 each carb) Slow Speed Adjustable N/Valves)
(J. Reeves)

The adjustment procedure of the carburetor slow speed needle valves follows. NOTE... if the needle valves turn too freely, replace the nylon bearing retainer (the nylon item at the front of the carb that the needle valve goes through first) with the newer type RED retainer #315232. If your engine has that weird linkage that connects all four of those needle valves, the newer RED retainers will enable you to discard that linkage. The RED retainers make it impossible for the needle valves to vibrate out of adjustment.

(Carburetor Adjustment - 2 Slow Speed Adjustable Needle Valves, each carburetor)

Initial setting is: All (4) Slow speed valves = seat gently, then open 1-1/2 turns.

Facing the carburetors, start with the top left needle valve, then the top right valve, then the bottom let valve, then the bottom right valve. It may be necessary to redo these steps to get the adjustments ideally set

Start engine and set the rpms to where it just stays running. In segments of 1/8 turns, start to turn the S/S needle valve in. Wait a few seconds for the engine to respond. As you turn the valve in, the rpms will increase. Lower the rpms again to where the engine will just stay running.

Eventually you'll hit the point where the engine wants to die out or it will spit back (sounds like a mild backfire). At that point, back out the valve 1/4 turn. Within that 1/4 turn, you'll find the smoothest slow speed setting.

Do not attempt to gradually adjust all four of the valves at the same time. Do one at a time until you hit the above response (die out or spit back), then go on to the next valve.

When you have finished the above adjustment, you will have no reason to move them again unless the carburetor fouls/gums up from sitting, in which case you would be required to remove, clean, and rebuild the carburetor anyway.

I'd use a fuel pressure gage, check fuel pressure, key on, engine off, first thing in the morning, 60--66 psi, spider fuel system. If you have the spider fuel stem, that system is noted for problems.
There is a service bulletin for cold start-up problems, caused by fuel poppet valves sticking. Once you get it started, it runs fine the rest of the day. The poppet cleaning procedure shows to be a shop procedure.

two ways: cranking the engine by turning the crank pulley bolt. Best done with valve cover off to verify full engine oil prime. The other economical way is by disabling the ignition and fuel pump (fuse removal) and cranking engine for 5 seconds, three times each.

Maybe a problem in the fuel pump circuit. Check fuel pressure with engine off, and key turned to on, not start. If no pressure, diagnose the pump circuit at the fuel pump relay. One terminal for the relay would be the power feed for the pump. The engine computer signals the relay on for 2 seconds with key on to prime the system, also signals during engine cranking.

12th inlet and 14 exhaust ,4cyl engine all valves add to 9 ,,example--- no1 down adjust no8 ----no2 down adjust no7 all values add to 9 simple if you take your time to count the valve thats down subtract from 9 and then adjust that number ,this system works on all engine regardless of what the haynes book says ,6 cyl engine then its 13 ,and a 8 cyl engine then 17 ,in cases of 16 valves in a 4 cyl engine then its still the same as two valves work as one ,simple

4.3 L engine crank position sensor is located on passenger side bottom of timing cover. plug should be around the front of the intake manifold.

you need feeler guage, youl need find the valve clearence to set it and adjust each one by using the rule of 9

Have you checked fuel pressure? You said TBI so it needs to be around 11-12-13 psi