HerrDeacon said:You need to remove some tension first from the cable. You can push back the that lever with your hand and you may have enough slack to remove it. Also, you'll need to loosen the lock nut holding the cable to the carb (top right of your picture). Then do the same with the other cable at the bottom.
SONIC. said:No turning.
Pull the cable until its vertical over the barrel so it goes in the slot, and then slide it sideways out.
Like deacon said you have to remove the nuts first.