How do you replace *THIS* cable?

[l008com]

On my mom's lawnmower, the end of the drive cable snapped. Its an older machine so if one snapped, the other is probably close. So I was going to replace both. But I was looking at this today.




So the cable that snapped is the one with the spiral housing around it. if you unbolt this clamp, you can see how that cable and housing would come right out.
But the OTHER cable is the throttle cable. It also has stoppers embeded on both ends of the cable. So how on earth do you replace that cable? It appears to be permanently threaded through that cable clamp in a way that can't be removed. Well you could remove it easy enough just by snipping the cable, but you wouldn't be able to install a new cable.

 

[ILENGINE]

The cable with the spiral conduit is replaced by loosening/removing the clamp to get the cable out the other plain cable that terminates through the plastic block is replaced by replacing the cable with the end block already attached.

model number of the the mower would allow us to look up parts and show what the part looks like