Final answer:
The nurse's knowledge is demonstrated when they encourage the child to imagine a peaceful and calming place.
Step-by-step explanation:
The scenario that demonstrates the nurse's knowledge when using guided imagery to relieve pain in pediatric clients is option b) Encouraging the child to imagine a peaceful and calming place. Guided imagery is a technique where the child is guided to imagine a safe and pleasant environment, which can help distract from the pain and promote relaxation. This technique has been shown to be effective in reducing pain perception in pediatric patients.