Final answer:
The nurse would conduct short-term counseling to help the client cope with the stress of hospitalization and concern for pet care.
Step-by-step explanation:
The type of counseling that the nurse would conduct in this situation is short-term counseling.
Short-term counseling is focused on providing immediate support and assistance to clients who are experiencing a specific issue or crisis, such as the stress of hospitalization and concern for pet care.
During short-term counseling, the nurse would work with the client to help identify coping strategies, explore options for pet care, and provide emotional support during their hospitalization period.