Final answer:
WPA2-Enterprise is the wireless security mode that offers both personal and enterprise authentication, with government-grade security.
Step-by-step explanation:
The wireless security mode that supports government-grade security and offers both personal and enterprise authentication is WPA2-Enterprise.
WPA2-Enterprise is the most secure level of Wi-Fi security and is commonly used by government organizations and large enterprises. It utilizes the 802.1X authentication framework for enterprise-level authentication and the Extensible Authentication Protocol (EAP) for securely exchanging authentication credentials.
With WPA2-Enterprise, individuals can authenticate using their own unique credentials, while organizations can centrally manage and control access to their wireless network.