Blockage in common bile duct will hamper delivery of bile juice in digestive tract. In absence of bile, fat digestion will not be possible.
Common bile duct is an anatomical connection between liver and duodenum of small intestine. Bile juice produced in liver is delivered to digestive tract and emulsifying action of bile breaks down large fat globules in microscopic spheres. Thus surface area of dietary fat increases drastically, and enzyme lipase can now act on it.
In case common bile duct is blocked (as happens in case of formation of stone or tumor) the bile will start accumulating in system. Some components of bile will also readily diffuse into blood to cause obstructive jaundice. Delivery of bile in duodenum would not be possible, thus fat digestion will not take place.