Watch the above video and pause it at 6:05. You can see that the carburetor pulls off at a 90 degree angle to the cables. If you look close you can see the 2 holes in the carburetor where the bolts went through and then at the top of the screen you can see the two bolts still attached to the engine. The bolt threads are gold colored. Most of these small engine carburetors are attached with 2 simple bolts with a gasket in between the carb and the engine. You can then watch him tilt the carb to tease that wire off
You are right that the hardest part is doing this under the van in an awkward position. That is why they charge a lot to do it
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