Ok, let's start from the beginning:
The throttle on a Honda or clone (such as a predator) Is governed to 3600rpm; whether you give it half or full throttle, it will only ever rev to a max 3600rpm. By pushing the lever under the tank you are manually overriding the governor which is NOT a good idea.
The governor can be adjusted slightly (to around 4000rpm) or removed completely; you can't simply disconnect it as there are plastic parts inside the engine the will explode & cause major damage to the internals of the engine.
The way we have all described is THE way to connect a cable to the throttle control...
As for which cable: One end of your cable needs to be cut off, which one depends on your pedal setup.
One you've removed one end of the inner cable, remove it from the outer, secure the end at the engine under the bracket on the throttle assenbly base plate & run the outer where it needs to be up to the pedal. Once your happy with the positioning, feed the inner cable through the pedal stop then through the outer cable up to the engine, feeding the end through the cable clamp on the throttle assembly.