Adjustment for throttle cable that hooks to the carb

I agree with Mike, year--make--model would help?
If this is an older carbed engine, no computer, if you get a carb kit, the kit will usually have the instructions for setting everything. As far as your throttle cable, I can't see anything from here. I guess, I'd have to look at it. Can you adjust the idle w/o the throttle cable then hook up the cable? Hopefully the idle stays the same?

You do not adjust the throttle cable, you adjust the idle speed hard stop screws with a carburetor manometer hooked up to the vacuum sync port on each carb.

I would check the throttle adjustment screw on the throttle assembly on handle bars. Be sure it is not screwed all the way in for max throttle. You can also check the carb and be sure that the idle screw is not adjusted for high idle as well. There may be an adjustment screw on carb for the cable stop.

The throttle cables aren't adjustable. Make sure the other end is on the trigger correctly and that it is routed through the handle and the engine cover correctly. Also, make sure the throttle shaft and throttle plate (inside carb) are free and easy in their movement with the throttle cable off. The engine idle speed adjusting screw may be in too far also. Back it all the way out and then back in with the throttle closed Once the speed screw touches the throttle lever (what you hook cable into) on the shaft, give it about 2 turns in. This is about all you can do. If the cable is stretched badly (rare), it would need to be replaced.

sounds like the throttle valve (TV) cable is adjusted wrong. Proper adjustment procedure: with engine warm and turned off find the adjuster fo TV cable. the cable is the one hooked to the bottom of the throttle lever on the carb, follow it back to the bracket, there will be a metal tab on top of the cable, depress this tab and push the black part of the cable where the wire comes out, toward the rear of the car, it should go all the way in. Now grab the throttle lever on the top where the throttle cable hooks up and push it wide open, it will be difficult, and you will hear some clicking from the TV cable bracket, once you get it wide open just release the throttle and the adjustment is done. If it does not shift correctly now have a trans shop look at it, as the TV cable is the only adjustment on this trans. All this info is assuming you have an overdrive trans, either 200r4 or 700r4.

Noadjustments can be made.Order the correct cables as needed through any GMparts dealership

First, follow your throttle cable down to the carb. Locate the clamp that holds the housing in place and loosen it just enough to move the cable. Start the mower and adjust the idle by the screw that touches the same plate that your cable hooks to. Then push the throttle control to idle and retighten the cable clamp.

The air mixture needle valve is on the Carb. Throttle screw as you call it, you might be referring to 1- throttle adjustment at the twist throttle hand grip. 2- At the top of the carb is a throttle cable adjustment 3- some times somewhere between the twist grip and the carb there is an adjustment.4- there is also a idle adjustment at the carb.

Your problem is probably the sycronizing as long as you havent messed with the fuel screw or jetting. If you dont have a set of vacuum guages you can eyeball the slides in the carbs to at least get you by and you can usually get them pretty close. Find the carb that is directly linked to the cable. the other carbs are adjustable to that carb so you need to make all the other carbs identical to that one. Look at the gap from the bottom of the slide to the bottom of the bore of the carb on that base carb with the throttle at idle bike not running. With the adjustments on the linkage to the other carbs adjust the other slides to the same height as that base carb as close as you can. Measure if possible to get all the carbs as close as possible to each other. you may have to adjust the idle after. If the adjustments on the carbs are all cables, for example there is a cable to each carb directly connected to the slide just adjust each cable accordingly and achieve the same as above. make sure you have a little freeplay at the throttle when you are done. you can adjust that by the cable adjustment by the throttle which will keep all the carbs in sync

Remove the old carb.  Bolt the new carb and gasket onto the manifold.  Hook up the fuel line and clamp.  Thread the throttle cable through the linkage and tighten.  Have someone hold the gas pedal to the floor, look inside the carb and make sure the throttle plate inside the carb is full open.  Next, wire in the electric choke, this should just clip on.
Now after the engine is running and warmed up...adjust the mixture and idle speed adjustments on the side of the carb.  Is this a two barreled cab and does it have a manual choke?