Aliver cell requires energy to move vitamins from an area of low concentration, across the cell membrane, to an area of high concentration. the process used by the liver cell is called

The process is called active transport.

Active transport is where materials will move from a region of lower concentration to the region of higher concentration, against the concentration gradient. Meanwhile, diffusion or osmosis is down the concentration gradient.

This process requires extra energy. Unlike diffusion or osmosis, they're achieved by natural tendency. Active transport also requires a carrier protein to bring the substances against the concentration gradient.

Therefore active transport is the answer.