**Core Concept**
The question is testing the management of chronic pancreatitis, specifically in the context of a dilated pancreatic duct and pancreatic stones. Chronic pancreatitis is a progressive inflammatory disease of the pancreas, often resulting from chronic alcohol abuse, leading to fibrosis, calcification, and ductal dilatation.

**Why the Correct Answer is Right**
The management of chronic pancreatitis involves both medical and surgical interventions. The presence of a dilated pancreatic duct and stones in the tail of the pancreas suggests that the patient has a complication of chronic pancreatitis, specifically pancreatic ductal dilatation and calculi. The most appropriate management in this scenario is endoscopic retrograde cholangiopancreatography (ERCP) with sphincterotomy and stone extraction. ERCP allows for direct visualization of the pancreatic duct and enables the removal of stones, which can provide relief from pain and improve pancreatic function.

**Why Each Wrong Option is Incorrect**
* **Option A:** Medical management with analgesics and pancreatic enzyme supplements may provide symptomatic relief but does not address the underlying cause of the patient's condition, which is the dilated pancreatic duct and stones.
* **Option B:** Surgical intervention, such as distal pancreatectomy, may be considered in cases of severe pancreatic disease, but it is not the most appropriate initial management for a patient with a dilated pancreatic duct and stones.
* **Option D:** Pancreatic transplantation is a radical procedure that is typically reserved for patients with severe pancreatic insufficiency and is not indicated in the management of chronic pancreatitis with a dilated pancreatic duct and stones.

**Clinical Pearl / High-Yield Fact**
Chronic pancreatitis is a progressive disease that can lead to pancreatic calcification, fibrosis, and eventually pancreatic insufficiency. Early recognition and management of complications, such as pancreatic ductal dilatation and calculi, are crucial to prevent further disease progression and improve quality of life.

**Correct Answer: C. ERCP with sphincterotomy and stone extraction.**