Final answer:
Children can typically respond to a dentist's instructions at the ages of 3-4 years, as they have developed the necessary language and cognitive skills.
Step-by-step explanation:
A child should first be able to respond to the dentist's instructions between the ages of 3-4 years old. By this age, children have developed sufficient language skills and cognitive abilities to understand and follow simple directions. Understanding how to respond to instructions from a dentist is essential for children as they begin regular dental visits and learn the importance of oral hygiene. Ensuring communication between the dentist and child helps in making the experience less intimidating and more productive for maintaining dental health.