Hi centxn, it looks to me as if your engine may have a design change not covered in the workshop manuals I have. Here is your picture of your carburetor, with the normal position of the idle speed adjustment screw circled in yellow:
[Linked Image]

As you can see, your carburetor just has the hole for the idle speed screw, but no screw is fitted. Can you tell us whether there is a thread in that hole please? Also, if you look at roebuck's picture of his GCV160 carburetor, you will see that it has a tang on the throttle butterfly bell crank for the idle speed screw to hold the throttle partly open (circled in red):
[Linked Image]

I cannot see in your picture, whether your carburetor has this tang.

If the throttle speed adjustment screw-hole has never been tapped, and your carburetor does not have the tang for the idle speed screw to press against, your engine may have a feature that is not found on any of the Honda engines I have seen to date. The feature is one that Briggs and Stratton call "governed idle", and it eliminates the idle speed adjustment screw, replacing it with a spring mechanism attached to the engine's governor, to control idle speed. On the other hand if your carburetor has a tapped idle speed screw hole, and a tang on the throttle butterfly bell crank for the idle speed screw to press against, it is much more likely that the idle speed adjustment screw is just missing from your carburetor. Hence we need to know more about your carburetor before we can proceed.

Note that the published Honda workshop manuals show an early version of the GCV160 carburetor, which I included in a previous post. roebuck's picture is of a later carburetor, not covered by the manuals, which is similar to yours but has provisions for an idle speed adjustment screw.

If you can show us enough detail, we can try to figure out whether you have missing parts, or alternatively, you have a governed idle system which we will then need to investigate and understand. It is fairly likely, if you have governed idle, that the choke mechanism is slightly out of adjustment and is simply causing the idle speed to be increased, but we will be able to resolve this if we see some additional pictures of the engine with the carburetor installed.