* **hear this** - "heard that Jesus began to teach in Galilee"
* **whether** - "if"
* **the man** - This refers to Jesus.
* **he discovered** - "Pilate discovered"
* **he was under Herod's authority** - The passage does not state the implied fact that Herod was the ruler of Galilee. You could make this information explicit: "Jesus was under the authority of Herod because Herod ruled over Galilee." (See: [[en:ta:vol1:translate:figs_explicit]])