**Core Concept**
The question is testing the concept of growth and development in children, specifically the rate of growth and the relationship between birth height and later heights. This is a fundamental aspect of pediatric medicine, and understanding these principles is crucial for assessing growth and development in children.

**Why the Correct Answer is Right**
At birth, a child's height is a good indicator of their genetic potential for growth. The rate of growth is fastest in the first two years of life, with an average increase of about 25 cm per year. By the age of 4, a child's height is approximately double their birth height. This is because the growth rate slows down after the age of 2, and by the age of 4, the child's growth pattern starts to resemble the adult growth pattern. This is why the correct answer is 4 years old.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it is too early for a child's height to double their birth height. By the age of 1-2 years, a child's height is still increasing rapidly, but it is not yet double their birth height.
* **Option B:** This option is incorrect because it is too late for a child's height to double their birth height. By the age of 5-6 years, a child's growth rate has slowed down significantly, and their height is not yet double their birth height.
* **Option D:** This option is incorrect because it is not a specific age and does not provide a clear answer.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the growth rate of children slows down after the age of 2, and by the age of 4, the child's growth pattern starts to resemble the adult growth pattern. This is a critical concept in pediatric medicine, and understanding it is crucial for assessing growth and development in children.

**Correct Answer: C. 4**