Final answer:
In the second half of the chapter, Smaug shows his vengeance by attacking Lake-town and mocking Bilbo and the dwarves.
Step-by-step explanation:
In the second half of the chapter, Smaug shows his vengeance through two main actions. Firstly, he attacks the town of Lake-town, burning its buildings and causing chaos and destruction. Secondly, he mocks and taunts Bilbo and the dwarves with his clever and ominous words, instilling fear in them and relishing in their powerlessness against him.
These actions demonstrate Smaug's desire for revenge and his enjoyment of causing harm and suffering to others.