**Core Concept**
In bacterial meningitis, empiric antibiotic therapy aims to cover the most likely pathogens, including *Streptococcus pneumoniae*, *Neisseria meningitidis*, and *Haemophilus influenzae* type b. The choice of antibiotic depends on the patient's age, vaccination status, and local epidemiology.

**Why the Correct Answer is Right**
For a six-month-old child, the preferred empiric antibiotic is a third-generation cephalosporin, such as cefotaxime or ceftriaxone, which provides broad-spectrum coverage against the common bacterial meningitis pathogens. This class of antibiotics is effective against *S. pneumoniae*, *N. meningitidis*, and *H. influenzae* type b, making it an ideal choice for empiric treatment in this age group. The intravenous route ensures rapid achievement of therapeutic concentrations in the cerebrospinal fluid.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not specified, so we cannot evaluate its correctness.
* **Option B:** This option is also not specified, so we cannot comment on its accuracy.
* **Option C:** This option is not specified, so we cannot determine its validity.

**Clinical Pearl / High-Yield Fact**
For empiric treatment of bacterial meningitis, it is crucial to consider the patient's age, vaccination status, and local epidemiology to choose the most appropriate antibiotic. For example, in areas with high incidence of penicillin-resistant *S. pneumoniae*, vancomycin may be added to the regimen.

**Correct Answer:** C. Ceftriaxone.