**Core Concept**
Meningitis due to H. influenzae can cause severe complications, including hearing loss, which is a result of the infection's impact on the inner ear. The essential step in discharge planning involves assessing the patient's auditory function to prevent further complications.

**Why the Correct Answer is Right**
The correct answer, **C. Bilateral evoked auditory response**, involves assessing the patient's hearing function using auditory evoked potentials, such as the auditory brainstem response (ABR) or the auditory nerve response (ANR). This test measures the electrical activity in the brain's auditory pathways in response to auditory stimuli and helps detect any hearing loss or abnormality. In patients with meningitis, especially those caused by H. influenzae, hearing loss can occur due to the infection's impact on the inner ear. Early detection and assessment of hearing function are crucial to prevent further complications and ensure proper rehabilitation.

**Why Each Wrong Option is Incorrect**
**Option A:** EBG (Electroencephalogram) is not directly relevant to the assessment of hearing function in patients with meningitis due to H. influenzae. While an EEG may be useful in assessing the patient's neurological status, it does not specifically address potential hearing loss.

**Option B:** Assessing development milestones is crucial in pediatric patients, but it is not directly relevant to the discharge planning of a patient with meningitis due to H. influenzae. Developmental assessment may be important in the long-term follow-up of patients with meningitis, but it is not an essential step in discharge planning.

**Option D:** Referring for physiotherapy may be necessary in patients with meningitis who have experienced weakness or paralysis, but it is not directly related to the assessment of hearing function in patients with meningitis due to H. influenzae.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that hearing loss can be a complication of meningitis due to H. influenzae, and early detection and assessment of hearing function are crucial to prevent further complications. A bilateral evoked auditory response test should be performed in all patients with meningitis to assess their auditory function.

**✓ Correct Answer: C. Bilateral evoked auditory response**