**Core Concept**
The question is testing the identification of a specific type of bacteria based on its antibiotic resistance pattern, growth characteristics, and biochemical properties. The organism in question is a gram-positive rod that is commonly found in the human gut and is known to cause intra-abdominal sepsis.

**Why the Correct Answer is Right**
The organism is resistant to vancomycin, gentamycin, and ampicillin, which suggests that it is a gram-positive rod that is not susceptible to beta-lactam antibiotics or aminoglycosides. The fact that it grows well in the presence of 6.5% NaCl suggests that it is a halophilic organism. The positive bile esculin hydrolysis test indicates that it is a member of the Enterococcus genus. The growth in the presence of arginine suggests that it is Enterococcus faecalis, which is a common cause of intra-abdominal sepsis.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because Enterococcus faecalis is not typically resistant to vancomycin.
* **Option B:** This option is incorrect because E. faecalis does not grow well in the presence of 6.5% NaCl.
* **Option C:** This option is incorrect because E. faecalis is not typically resistant to gentamycin.
* **Option D:** This option is incorrect because E. faecalis is not typically resistant to ampicillin.

**Clinical Pearl / High-Yield Fact**
Enterococci, particularly E. faecalis, are known to be resistant to multiple antibiotics due to their ability to acquire antibiotic resistance genes. They are commonly found in the human gut and can cause intra-abdominal sepsis, especially in patients with compromised immune systems.

**Correct Answer:** B. Enterococcus faecalis.