How do the liver and pancreas work together to maintain blood glucose levels at 4.5 mM?

By using the secretion of insulin and glucagon.

Explanation:

When the level of glucose in blood is high the pancreas secretes insulin that sends a negative feedback signal to the liver to absorb glucose. Synthesis of fats is initiated, glucose transported to the muscles and adipocytes for storage through glycogenolysis.

When the levels of glucose are too low in the blood, the pancreas secretes glucagon to initiate the breakdown of glycogen by the liver.