Final answer:
The correct pathway for a secretory protein within a eukaryotic cell is Endoplasmic reticulum to Golgi apparatus and then to Secretory vesicles, where the protein is synthesized, modified, and packaged before being sent to its destination.
Step-by-step explanation:
The most probable pathway for processing and packaging a secretory protein within a eukaryotic cell is: Endoplasmic reticulum -> Golgi apparatus -> Secretory vesicles. This pathway begins with the synthesis of the protein on bound ribosomes into the rough ER lumen. From there, the proteins travel to the Golgi apparatus via a vesicle, where they undergo modification and sorting. Finally, they are packaged into secretory vesicles and ready to be transported to their final destinations outside the cell through exocytosis or to other areas within the cell.