Final answer:
The order of insects where back wings are not membranous is the Coleoptera or beetles, which have hard front wings, called elytra, that serve as protection for their membranous hindwings and abdomen.
Step-by-step explanation:
The insect order where the back wings are not membranous is the Coleoptera, commonly known as beetles . In beetles, the front pair of wings is hardened into shell-like structures called elytra which protect the membranous hindwings as well as the abdomen when the beetle is not flying.
The elytra are not used for flying but open up to allow the hindwings to come out and function during flight. Beetles' adaptation is unique among winged insects, as they have evolved to use their wings not just for flight but also as protective covers.
Other insects, such as butterflies, mayflies, and dragonflies, have wings that are typically thin and membranous. Unlike a beetle's elytra, these wings are used directly for flight and do not serve as a protective covering for body parts.