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One of the core envisions of the sixth-generation (6G) wireless networks is to accumulate artificial intelligence (AI) for autonomous controlling of the Internet of Everything (IoE). Particularly, the quality of IoE services delivery must be maintained by analyzing contextual metrics of IoE such as people, data, process, and things. However, the challenges incorporate when the AI model conceives a lake of interpretation and intuition to the network service provider. Therefore, this paper provides an explainable artificial intelligence (XAI) framework for quality-aware IoE service delivery that enables both intelligence and interpretation. First, a problem of quality-aware IoE service delivery is formulated by taking into account network dynamics and contextual metrics of IoE, where the objective is to maximize the channel quality index (CQI) of each IoE service user. Second, a regression problem is devised to solve the formulated problem, where explainable coefficients of the contextual matrices are estimated by Shapley value interpretation. Third, the XAI-enabled quality-aware IoE service delivery algorithm is implemented by employing ensemble-based regression models for ensuring the interpretation of contextual relationships among the matrices to reconfigure network parameters. Finally, the experiment results show that the uplink improvement rate becomes 42.43% and 16.32% for the AdaBoost and Extra Trees, respectively, while the downlink improvement rate reaches up to 28.57% and 14.29%. However, the AdaBoost-based approach cannot maintain the CQI of IoE service users. Therefore, the proposed Extra Trees-based regression model shows significant performance gain for mitigating the trade-off between accuracy and interpretability than other baselines.