The widespread use of intelligent devices and the emergence of 6G networks have led to a massive amount of edge data being produced in a distributed manner, bringing forth a pressing need for privacy-preserving and communication-efficient learning. Federated learning (FL) enables collaborative model training without sharing raw data, but it suffers from challenges such as high communication overhead, non-IID data distribution, straggling devices, and rigid offloading strategies in wireless communication environments. Recent works have attempted to address these issues using device-to-device (D2D) communication or edge server-based approaches; however, achieving both communication efficiency and high learning performance remains a significant challenge. In this work, a hybrid federated learning architecture for D2D-enabled 6G networks is proposed, integrating adaptive D2D communication and edge server offloading to enhance both learning efficiency and communication performance. The proposed framework incorporates channel awareness and federated averaging to ensure robust global model aggregation under non-IID data conditions. Extensive simulation results on the EMNIST Digits dataset demonstrate that the proposed approach achieves a final accuracy of 97.41% with an average accuracy of 93.98%, while significantly reducing communication cost across federated learning rounds. Furthermore, the results illustrate adaptive hybrid communication behavior with approximately 60% D2D communication and 40% edge offloading. Comparative analysis with existing federated learning methods confirms the effectiveness, scalability, and suitability of the proposed framework for next-generation 6G-enabled intelligent edge networks.