The insect order which is capable of flying in both forward and backward direction is

The insect order which is capable of flying in both forward and backward directions is Odonata.
Odonata is an order of flying insects that includes dragonflies and damselflies. These insects characteristically have large rounded heads covered mostly by well-developed, compound eyes, which provide good vision, legs that facilitate catching prey in flight, two pairs of long, transparent wings that move independently, and elongated abdomens.
They have three ocelli and short antennae. The mouthparts are on the underside of the head and include simple chewing mandibles in the adult.