Final answer:
The client demonstrates an understanding of home infection prevention teaching if they express actions such as regular hand washing and not sharing personal items that could transmit infections.
Step-by-step explanation:
A statement by the client that indicates an understanding of the home infection prevention teaching for someone who is HIV positive would be one that reflects good practices for avoiding infections. Such a statement may include rigorous hand hygiene, avoiding exposure to people with contagious illnesses, properly preparing and storing food to prevent foodborne illnesses, and staying up-to-date with vaccinations to prevent infections.
For instance, a clear indication of understanding might be the client saying, "I will make sure to wash my hands regularly and avoid sharing personal items like toothbrushes or razors." This shows the client is aware of the importance of maintaining good personal hygiene and avoiding practices that could lead to transmission of infectious agents.