**Core Concept**
The patient's symptoms and physical examination findings are suggestive of gallbladder disease, specifically gallstones causing intermittent biliary colic. The hepatoduodenal ligament contains the bile ducts, which are anatomically related to the gallbladder.

**Why the Correct Answer is Right**
The hepatoduodenal ligament is a fibrous fold of the peritoneum that connects the liver to the duodenum. It contains the common bile duct, the hepatic artery, and the portal vein. As the surgeon inserts his fingers from right to left behind the hepatoduodenal ligament, he would be entering the **common bile duct**. This is a critical anatomical structure that is closely related to the gallbladder and is often involved in gallstone disease.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the **hepatic artery** is a vessel that supplies blood to the liver, but it is not the structure that the surgeon would be entering behind the hepatoduodenal ligament.

**Option B:** This option is incorrect because the **portal vein** is a vessel that brings blood from the gastrointestinal tract to the liver, but it is not the structure that the surgeon would be entering behind the hepatoduodenal ligament.

**Option D:** This option is incorrect because the **hepatic veins** drain blood from the liver to the inferior vena cava, but they are not located behind the hepatoduodenal ligament.

**Clinical Pearl / High-Yield Fact**
When performing a cholecystectomy (gallbladder removal), the surgeon must take care to identify and preserve the common bile duct, which is a critical structure that carries bile from the liver to the small intestine.

**Correct Answer:** C.