Branch-tracing shortcut. Start from the celiac trunk, which splits into three: left gastric, splenic, and common hepatic. Anything you can reach by walking down only the common hepatic limb will lose its supply when that limb is tied. From the common hepatic come the right gastric artery and the gastroduodenal artery, and from the gastroduodenal comes the right gastroepiploic artery. Both therefore sit on the hepatic side. Now disqualify the distractors: the left gastric is a sibling branch of the celiac trunk and is fed independently, while the short gastric arteries hang off the splenic artery, the other celiac sibling. Neither is downstream of the hepatic artery. So the pair that loses flow is the right gastric and right gastroepiploic. In practice rich anastomoses (gastric arcades) often keep the stomach alive, but anatomically these two are the hepatic-dependent vessels. Reference: Gray's Anatomy, 41e, pp 1116-1117.