Final answer:
The nobleman's son in John 4:46 lay sick in the town of Capernaum, a place where Jesus performed many miracles.
Step-by-step explanation:
In John 4:46, the son of a certain nobleman lay sick in Capernaum. The verse narrates the account of a royal official who implored Jesus to come and heal his son, who was gravely ill. Capernaum, situated near the Sea of Galilee, is mentioned as the location where the nobleman's son was ailing.
The narrative highlights the desperation and faith of the nobleman, who sought Jesus' intervention for his son's healing, ultimately leading to a demonstration of Jesus' miraculous power even at a distance, as the nobleman's son was healed when Jesus declared the word from afar.