The hepatic portal vein, option 4, is the correct answer. It is responsible for carrying nutrient-rich blood from the stomach and small intestines to the liver. It allows the liver to regulate the distribution and balance of nutrients in the body and filter toxins.

Option 1 and 3, the left and right hepatic arteries, are part of the liver`s main blood supply, but they supply oxygenated blood from the heart to the liver, not nutrient-rich blood from the gastrointestinal tract to the liver.

Option 2, the hepatic vein, is involved with moving deoxygenated blood from the liver back to the heart through the inferior vena cava, not with delivering nutrient-rich blood to the liver. So, while these options are all important for liver function, they don`t answer the question as accurately as the hepatic portal vein.