The principal action of enterokinase in human intestinal juice is to activate trypsinogen in the pancreatic juice. Trypsinogen is an inactive form of the enzyme trypsin, which is necessary for the digestion and breakdown of proteins. Enterokinase acts on trypsinogen by cleaving a peptide bond, resulting in the activation of trypsinogen into trypsin.

Option 1, hydrolyzing casein into paracasein, is incorrect. Casein is primarily broken down by the enzyme rennin, not enterokinase.

Option 2, acting on the terminal peptide bond of a peptide chain to release the last amino acid, is also incorrect. This role is typically carried out by carboxypeptidases, not enterokinase.

Option 3, converting pro-carboxypeptidase to carboxypeptidase, is not the principal action of enterokinase. While enterokinase can activate other pancreatic enzymes, its primary role is the activation of trypsinogen.

The correct answer is option 4, as stated above.