Final answer:
The nurse must first assess the client with a new onset of difficulty breathing, as this situation requires immediate intervention and can potentially be life-threatening.
Step-by-step explanation:
In prioritizing client care, the nurse must assess and address the most critical needs first, according to the principles of triage. In this scenario, the client with a new onset of difficulty breathing should be assessed first as this could indicate a life-threatening situation such as a pulmonary embolism, asthma attack, or another acute respiratory condition. Difficulty breathing requires immediate attention to prevent further deterioration of the client's health status.
An anxious client who is 3 days post myocardial infarction requires monitoring and intervention to manage anxiety, but unless there are signs of acute distress, this is less immediately life-threatening compared to difficulty breathing. The client with type 2 diabetes mellitus might have concerns that require attention, but without additional information suggesting an emergency, this need is not as urgent as respiratory distress. Similarly, a client whose blood transfusion is near completion should be monitored for reactions, but typically, immediate post-transfusion reactions would have already been identified.