Final answer:
The correct method for instilling eye drops in a child is to place them in the conjunctival sac as the lower lid is pulled down, ensuring the medicine is distributed safely and comfortably.
Step-by-step explanation:
The nurse should administer eye drops to a 6-year-old child in the conjunctival sac as the lower lid is pulled down. This method avoids direct contact with the cornea or the anterior surface of the eyeball, which can be prone to injury and discomfort. Instead, placing the drops in the conjunctival sac allows for the liquid to be distributed evenly across the eye when the child blinks, without causing unnecessary distress or damage to the eye's sensitive structures.