Final answer:
The nurse should report the incident to the supervisor immediately to ensure patient safety and appropriate handling of the situation.
Step-by-step explanation:
If another nurse arrives for duty with alcohol on her breath, the nurse's first action should be to report the incident to the supervisor. Confronting the nurse immediately might lead to a conflict and ignoring the situation could endanger patient safety. Offering a breath mint does not address the seriousness of the issue. It is important for the safety of patients that the supervisor is informed so that professional steps can be taken to handle the situation accordingly.