**Core Concept**
The question is testing the knowledge of the most common cause of acute bacterial meningitis in a specific age group, which is a critical aspect of **infectious disease** and **neurology**. The underlying principle involves understanding the **pathogenesis** of bacterial meningitis and the typical **causative agents** in different age groups.

**Why the Correct Answer is Right**
Given the age of the patient (15 years old) and the presentation of severe headache and purulent nasal discharge leading to acute bacterial meningitis, the most likely etiological agent is *Neisseria meningitidis*. This bacterium is a common cause of meningitis in adolescents and young adults, often associated with **epidemics** in closed communities such as schools or military barracks.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because, although *Streptococcus pneumoniae* is a common cause of bacterial meningitis, it is more typically seen in other age groups or contexts.
**Option B:** Incorrect as *Haemophilus influenzae* type b (Hib) is more commonly associated with meningitis in younger children, especially before widespread vaccination.
**Option D:** Incorrect because, while *Escherichia coli* can cause meningitis, it is less common in this age group and more often associated with neonatal meningitis or specific predisposing conditions.

**Clinical Pearl / High-Yield Fact**
It's crucial to remember that *Neisseria meningitidis* can cause outbreaks, especially in settings like schools or dormitories, and vaccination is an effective preventive measure.

**Correct Answer:** D. Neisseria meningitidis