Final answer:
An 18-month-old patient should be placed in the right lateral recumbent position for the administration of ear drops to the right ear, allowing for proper delivery of the medication.
Step-by-step explanation:
The correct position to place an 18-month-old patient when administering ear drops to the right ear is the right lateral recumbent position. In this position, the child lies on their left side, which allows the right ear to face upward and makes it easier to administer the drops without them quickly draining out. This position helps in targeting the ear canal properly and ensures that the medication is delivered effectively.