**Core Concept**
The common hepatic artery is a vital branch of the celiac trunk that supplies blood to the liver, stomach, and nearby structures. It divides into the proper hepatic artery, left gastric artery, and right gastric and right gastroepiploic arteries. Understanding the anatomy of the hepatic artery and its branches is crucial for surgical procedures and managing vascular injuries.

**Why the Correct Answer is Right**
Ligation of the common hepatic artery will compromise blood flow to the right gastric artery and the right gastroepiploic artery. This is because the common hepatic artery gives rise to the right gastric artery, which supplies the lesser curvature of the stomach, and the right gastroepiploic artery, which supplies the greater curvature of the stomach. The left gastric artery, which is also a branch of the common hepatic artery, primarily supplies the upper part of the lesser curvature of the stomach. The right and left gastric arteries, as well as the short gastric arteries, receive their blood supply from the splenic artery, not the common hepatic artery.

**Option A:** The right and left gastric arteries receive their blood supply from the left gastric artery, not the common hepatic artery. Therefore, ligation of the common hepatic artery will not compromise blood flow to these arteries.
**Option B:** The short gastric arteries receive their blood supply from the splenic artery, not the common hepatic artery. Therefore, ligation of the common hepatic artery will not compromise blood flow to these arteries.
**Option C:** The right gastroepiploic artery is a branch of the common hepatic artery, but the short gastric arteries receive their blood supply from the splenic artery. Therefore, ligation of the common hepatic artery will compromise blood flow to the right gastroepiploic artery but not the short gastric arteries.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the common hepatic artery and the splenic artery arise from the celiac trunk, but they supply different structures. The common hepatic artery supplies the liver, stomach, and nearby structures, while the splenic artery supplies the spleen, pancreas, and stomach.

✓ Correct Answer: D. Right gastric and right gastroepiploic aery