In this paper, we focus on offloading a computing task from a user equipment (UE) to a multi-access edge computing (MEC) server via multi-hop relaying. We assume a general relaying case where relays are energy-constrained devices, such as other UEs, internet of things (IoT) devices, or unmanned aerial vehicles. To this end, we formulate the problem as a minimization of the sum energy consumed by the energy-constrained devices under the constraint on the maximum requested time of the task processing. Then, we propose a multi-hop relaying combining half and full duplexes at each individual relay involved in the offloading. We proof that the proposed multi-hop relaying is convex, thus it can be optimized by conventional convex optimization methods. We show our proposal outperforms existing multi-hop relaying schemes in terms of probability that tasks are processed within required time by up to 38\% and, at the same time, decreases energy consumption by up to 28%.