Final answer:
The lymph vessels from the splenic hilum drain into the right subclavian vein via the right lymphatic duct or into the thoracic duct on the left side.
Step-by-step explanation:
The lymph vessels drain into the thoracic duct or the right lymphatic duct depending on the side of the body. On the right side, the lymph fluid from the splenic hilum drains into the right subclavian vein via the right lymphatic duct. On the left side, the remaining portions of the body drain into the thoracic duct, which also drains into the left subclavian vein.