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Fog computing is one of the major components of future 6G networks. It can provide fast computing of different application-related tasks and improve system reliability due to better decision-making. Parallel offloading, in which a task is split into several sub-tasks and transmitted to different fog nodes for parallel computation, is a promising concept in task offloading. Parallel offloading suffers from challenges such as sub-task splitting and mapping of sub-tasks to the fog nodes. In this paper, we propose a novel many-to-one matching-based algorithm for the allocation of sub-tasks to fog nodes. We develop preference profiles for IoT nodes and fog nodes to reduce the task computation delay. We also propose a technique to address the externalities problem in the matching algorithm that is caused by the dynamic preference profiles. Furthermore, a detailed evaluation of the proposed technique is presented to show the benefits of each feature of the algorithm. Simulation results show that the proposed matching-based offloading technique outperforms other available techniques from the literature and improves task latency by 52% at high task loads.