Final answer:
Assign the nursing assistant to the stable elderly client with a thyroidectomy four days ago since they require care that fits the assistant's scope of practice.
Step-by-step explanation:
The nursing assistant should be assigned to care for the elderly client with a thyroidectomy four days ago. This patient is likely to be the most stable and require tasks within the scope of a nursing assistant's practice, such as assisting with activities of daily living, taking vital signs, and providing encouragement for mobility. In contrast, the 18-year-old with fractured vertebrae, the infant with meningitis, and the client with a thoracotomy would all require more complex care that should be managed by professional nursing staff due to the potential for serious complications and the need for specialized assessment and interventions.