In which of the following organisms, the respiration does not take place through cell membrane or skin?

Electric eels have gills, but they inhale air directly through their mouth and provide oxygen to the blood which is then transported to all the cells of the body.

Electric eels are obligate air breathers, which means they surface for air periodically. 

Their mouths are heavily vascularized with folds that increase the surface area, allowing them to breathe air, rather than trying to meet their respiration needs through gills in warm, anoxic waters(water that is depleted of dissolved oxygen).