Final answer:
The nurse should administer the pain medication as pain is subjective and the client's vital signs are stable, indicating no contraindications.
Step-by-step explanation:
If a client is prescribed pain medication every 4 to 6 hours as needed and requests it, even while appearing to be in good spirits and showing vital signs within normal ranges, the nurse's most appropriate action would be to administer the pain medication. Pain is a subjective experience and cannot be accurately assessed solely on the appearance or vital signs of the patient. It is essential to trust the client's report of pain and administer the prescribed medication as directed unless there are clear contraindications or reasons to believe the medication could harm the client.