I cannot gather from your post the reason for replacing the cable however if the cable is still in tact you firstly need to get max play on cable, meaning turning adjuster near your throttle completely inwards(this helps alot as you want your inner cable to be as long as possible). I can gather you have already removed slide from carb so then you need to grab hold of spring and pull it right back towards cap(compress spring) and pinch onto inner cable in front of compressed spring, push inner cable inwards towards slide and pull slightly to hollow side of slide, she should come unhooked. It is tricky however I sure you will get the hang of it. The more you do it the easier it becomes!