**Core Concept**
The management of a retained stone in the distal common bile duct involves a careful balance between the risks of surgery, the potential for complications, and the likelihood of successful removal. The goal is to achieve complete stone clearance while minimizing the risk of pancreatitis, cholangitis, and other complications.

**Why the Correct Answer is Right**
Endoscopic retrograde cholangiopancreatography (ERCP) with sphincterotomy is the preferred treatment for a retained stone in the distal common bile duct. This procedure involves using a flexible endoscope to visualize the bile ducts and perform a sphincterotomy, which allows for the safe removal of the stone. The sphincterotomy also helps to prevent the stone from passing back into the bile ducts. The use of ERCP with sphincterotomy has been shown to be effective in achieving complete stone clearance and reducing the risk of complications.

**Why Each Wrong Option is Incorrect**
**Option A:** Surgical exploration of the bile ducts is an option for the management of a retained stone, but it is generally reserved for cases where ERCP is not possible or has failed. This approach carries a higher risk of complications and is typically associated with longer hospital stays and recovery times.

**Option B:** Conservative management with antibiotics and observation is not a recommended approach for a retained stone in the distal common bile duct. This approach carries a high risk of complications, including cholangitis and pancreatitis, and is unlikely to result in successful stone clearance.

**Option C:** Percutaneous transhepatic biliary drainage (PTBD) may be used in some cases to manage complications related to a retained stone, but it is not a first-line treatment for stone removal. PTBD carries a risk of bleeding and bile leakage, and is typically used in cases where ERCP is not possible or has failed.

**Clinical Pearl / High-Yield Fact**
ERCP with sphincterotomy is a highly effective treatment for retained stones in the distal common bile duct, with a success rate of over 90%. However, it is essential to carefully select patients for this procedure, as it carries a risk of complications, including pancreatitis and bleeding.

**Correct Answer:** C.