Final answer:
Acute viral hepatitis is a likely cause of postoperative unconjugated hyperbilirubinemia, resulting from the liver's inability to conjugate bilirubin due to hepatocyte damage.
Step-by-step explanation:
A likely cause of postoperative unconjugated hyperbilirubinemia is acute viral hepatitis. Unconjugated hyperbilirubinemia occurs when the liver is unable to effectively conjugate bilirubin, which can be due to damage caused by infections such as viral hepatitis. When hepatocytes are damaged, the liver's ability to conjugate and excrete normally produced bilirubin is impaired, leading to elevated levels of unconjugated bilirubin in the blood.