Step 1: Interpret the clinical clues. Prolonged jaundice (unconjugated, persisting beyond 2-3 weeks) plus an umbilical hernia in a neonate is the classic combination pointing to congenital hypothyroidism.
Step 2: Mechanism. Thyroid hormone deficiency slows hepatic glucuronyl transferase activity and bowel transit, prolonging unconjugated hyperbilirubinaemia. Reduced muscle tone and connective-tissue laxity of the abdominal wall produce the umbilical hernia. Other features include lethargy, poor feeding, constipation, large fontanelle, macroglossia, hypothermia and hoarse cry.
Step 3: Why the others are wrong. Down syndrome can have an umbilical hernia and even coexisting hypothyroidism, but the specific dyad of prolonged jaundice + umbilical hernia classically denotes hypothyroidism. Cerebral palsy is a motor disorder and does not cause jaundice. Biliary atresia gives conjugated jaundice with pale stools, not this picture.
Key fact: Prolonged neonatal jaundice with umbilical hernia = congenital hypothyroidism; screen with TSH/T4.