The idle mixture screw (which Honda calls the pilot screw) should be set to 2 turns. Note that on those Keihin BE carburetors, used on GXV120, 140 and 160 Hondas, the idle jet may be a bit prone to getting clogged. I've covered the cleaning procedure in another thread: https://www.outdoorking-forum.com.au/forum/u...p;Words=gcv160&Search=true#Post38603
Note that the thread describes cleaning procedure for both the Keihin BE used on the OHV engines and the cheaper version used on the OHC engines. Here is a video showing how to clean the BE carburetor properly:
With regard to your original problem with idle speed, is the idle speed screw making contact with the idle stop when the speed control is set to idle? I notice that your governor spring is not in the hole shown in the workshop manual, at the speed control lever end:
Did you check that the governor arm is correctly set in relation to its shaft?
If you have issues or questions regarding the engine, please post them so that we can try to sort them out.