At the end of the three days, Esther goes to visit the king. He holds out his golden scepter to her, meaning that he's giving her permission to be in his court (i.e., he's not gonna kill her).
Despite having not seen her in thirty days, the king is glad to see her. He offers to give her whatever she wants, even half his kingdom.
She asks that the king and Haman join her at a banquet she's prepared for them today—so they do.
At the end of the banquet, the king asks Esther if she would like anything else. She says she would like to have another banquet with the king and Haman again, tomorrow. The king grants her request.
Haman leaves the banquet in high spirits. He's pretty pleased with himself and feels honored that Esther (who he doesn't know is Jewish) chose to invite him alone to eat with her and the king.
However, he runs into Mordecai, who is sitting at the king's gate. Mordecai still refuses to bow to him.
Enraged, Haman heads home, assembling his wife and his friends. He tells them about all the honors he's received and how the queen wanted to dine with him and everything—but it's still no use, as long as Mordecai won't respect him.
They advise him, telling him to build a massive gallows (fifty cubits, or seventy-five feet high) on which to hang Mordecai.
Haman is pleased with this advice. He builds the unnecessarily large gallows, thinking he'll execute Mordecai the following morning.