Cloud-fog computing frameworks are innovative frameworks that have been designed to improve the present Internet of Things (IoT) infrastructures. The major limitation for IoT applications is the availability of ongoing energy sources for fog computing servers because transmitting the enormous amount of data generated by IoT devices will increase network bandwidth overhead and slow down the responsive time. Therefore, in this paper, the Butterfly Spotted Hyena Optimization algorithm (BSHOA) is proposed to find an alternative energy-aware task scheduling technique for IoT requests in a cloud-fog environment. In this hybrid BSHOA algorithm, the Butterfly optimization algorithm (BOA) is combined with Spotted Hyena Optimization (SHO) to enhance the global and local search behavior of BOA in the process of finding the optimal solution for the problem under consideration. To show the applicability and efficiency of the presented BSHOA approach, experiments will be done on real workloads taken from the Parallel Workload Archive comprising NASA Ames iPSC/860 and HP2CN (High-Performance Computing Center North) workloads. The investigation findings indicate that BSHOA has a strong capacity for dealing with the task scheduling issue and outperforms other approaches in terms of performance parameters including throughput, energy usage, and makespan time.