duct that carries bile from the liver to the bile duct on its way to the duodenum

The duct that conveys bile from the liver to the gallbladder.

A duct that carries bile from the liver into the common bile duct which conveys it to the duodenum (the upper part of the small intestine). There are three hepatic ducts: the right hepatic duct (which drains bile from the right half of the liver); the left hepatic duct (which drains bile from the left half of the liver); and the common hepatic duct (which is formed by the junction of the right and left hepatic ducts).

The duct that carries bile away from the liver lobes and toward the union with the cystic duct.

the liver excretory duct, joins with gall bladder cystic duct to form the common bile duct. (More? Gastrointestinal Tract - Liver | GIT Notes)