Mechanisms of breathing vary among different groups of animals...

Lower invertebrates like sponges, coelenterates, and flatworms exchange $O_2$ with $CO_2$ by simple diffusion over their entire body surface. They do not possess specialized respiratory structures like gills.

Earthworms use their moist cuticle for respiration.

Insects have a network of tubes called tracheal tubes to transport atmospheric air within the body.

Special vascularised structures called gills are used by most aquatic arthropods and molluscs.

Therefore, the match between flatworms and gills is incorrect.

Answer: Flatworms – Gills