This paper explores the integration of Cybertwin technology within 6G networks to revolutionize healthcare delivery. It aims to enhance real-time monitoring, decision-making, and resource management through the Service-based Hierarchical Framework for Cybertwins in sixth-generation networks. The paper addresses the deployment challenges and proposes system theory as a comprehensive framework for designing complex interactions among healthcare-assigned Cybertwins. The article highlights the role of Cybertwin technology in advancing healthcare solutions, promising improved patient care and operational efficiency. It examines the current network setups and the potential of 6G infrastructure, discussing network topology optimization, theoretical modelling, and future directions. The paper underlines the transformative impact of combining 6G and Cybertwin technologies on healthcare, from high-definition telemedicine to large-scale patient monitoring. The paper further acknowledges the implementation challenges, such as technical complexity, security, and interoperability.