Final answer:
The nurse demonstrates technical skill by starting a new intravenous site and priming the infusion tubing.
Step-by-step explanation:
The technical skill demonstrated by the nurse in this situation is option A, starting a new, large-gauge intravenous site on the client and priming the infusion tubing. This skill is important because it ensures that the packed red blood cells can be safely and effectively administered to the client. By starting a new intravenous site, the nurse minimizes the risk of infection and provides a secure access point for the transfusion. Priming the infusion tubing ensures that there are no air bubbles or other contaminants that could be introduced into the client's bloodstream during the transfusion.