Final answer:
A client with the ability to recall more detail in remote memories than recent ones, vaguely recognize staff, and use memory aids with maximum assistance is at Rancho Los Amigos Level VI.
Step-by-step explanation:
The Rancho Los Amigos level described in the question refers to the cognitive functioning scale used to assess individuals after a brain injury. Based on the described abilities, such as demonstrating more depth and detail to remote memories than recent memories, having vague recognition of staff, and the ability to use assistive memory aid with maximum assistance, this pertains to Rancho Los Amigos Level VI. At this stage, clients show emerging awareness of appropriate response to self, family, and basic needs, such as eating or walking, but responses may be incorrect due to memory problems. At Level VI, they can attend to highly familiar tasks in a non-distracting environment for about 30 minutes with moderate redirection.