**Core Concept**
The question is testing the knowledge of the most common causative agent of meningitis in infants and young children, which is a critical aspect of pediatric infectious diseases. The correct answer is related to the pathogenesis of bacterial meningitis in this age group.

**Why the Correct Answer is Right**
The most common causative agent of meningitis in the age group of 6 months-3 years is *Haemophilus influenzae type b (Hib)*. This is due to the fact that Hib is a highly virulent bacterium that can invade the bloodstream and cross the blood-brain barrier to cause meningitis. The bacteria produce a polysaccharide capsule that helps them evade the host's immune system. In the past, Hib meningitis was a leading cause of morbidity and mortality in young children, but widespread vaccination has significantly reduced its incidence.

**Why Each Wrong Option is Incorrect**
* **Option A:** Streptococcus pneumoniae is a common cause of meningitis, but it is more commonly seen in older children and adults. It is not the most common causative agent in the 6 months-3 year age group.
* **Option B:** Neisseria meningitidis is a common cause of meningitis, but it is more commonly seen in adolescents and young adults. It is not the most common causative agent in the 6 months-3 year age group.
* **Option D:** Escherichia coli is a rare cause of meningitis in children, and it is more commonly seen in neonates and older children. It is not the most common causative agent in the 6 months-3 year age group.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that Hib meningitis is a medical emergency that requires prompt treatment with antibiotics and supportive care. Vaccination against Hib is highly effective in preventing meningitis and other invasive diseases caused by this bacterium.

**Correct Answer:** C. Haemophilus influenzae type b (Hib).