The majority of triglyceride digestion occurs in the small intestine facilitated by the enzyme

pancreatic lipase

Explanation:

Enzymes from pancreas involved in triacylglycerol digestion are called pancreatic lipases and they catalyze the partial hydrolysis of triglycerides into a mixture of free fatty acids and acylglycerols. After digestion of lipids, monoglycerides and fatty acids associate with bile salts and phopholipids to form micelles. Micelles are structures that are necessary for the transport the poorly soluble monoglycerides and fatty acids to the surface of the enterocyte. But, micelles cannot be absorbed by epithelial cell, only freely dissolved monoglycerides and fatty acids can. Free fatty acids and monogycerids can just diffuse across the plasma membrane because of their nonpolar nature.

Some absorption (e. g. for cholesterol) may be facilitated by specific transport proteins.