Final answer:
A phlebotomist should use a butterfly needle when a patient's hand is difficult to access for venipuncture.
Step-by-step explanation:
If a patient's hand is difficult to access, a phlebotomist might use a butterfly needle, which is a small, winged needle that is easier to maneuver in tight spaces. This needle, also known as a winged infusion set, is designed for precision and can be particularly useful when veins are difficult to puncture or when the patient has fragile, small, or rolling veins. When using a butterfly needle, the phlebotomist must be skilled and gentle to ensure a successful venipuncture with minimal discomfort to the patient.