Final answer:
Liver cells take in cholesterol from HDL primarily through the action of the SR-BI receptor and, to some extent, with the modification of HDL by hepatic lipase. Phagocytosis is not involved in this process, and an 'E receptor' is not a recognized participant in HDL cholesterol uptake.
Step-by-step explanation:
Cells in the liver take in cholesterol from high-density lipoprotein (HDL) primarily through a process facilitated by special receptors on the cellular surface. One such method is receptor-mediated endocytosis, which involves the liver's SR-BI receptor, also known as the scavenger receptor class B type I. However, phagocytosis is not typically involved in this transport of cholesterol from HDL to the liver. In terms of enzymes, hepatic lipase can act on HDL, modifying it to facilitate cholesterol uptake, but it is not the means by which cells directly take in cholesterol. On the other hand, an E receptor does not correspond to a known receptor involved in cholesterol uptake from HDL.
Therefore, the correct answers are Hepatic lipase and SR-BI receptor for the mechanisms through which cells take in cholesterol from HDL at the liver.