The duke's reply is somewhat complicated. At first he demands to know who stole Brabantio's Desdemona and that he will "throw the bloody book of law" at the culprit. When Brabantio names Othello, the duke begins to backpedal a bit. He has news that the Turks are attacking, and he needs his top general, Othello, to battle the Turks. He certainly does not want to throw Othello in jail! So, he asks Othello for his side of the story.
Othello cleverly requests that the duke send for Desdemona and let her tell whether or not her elopement with Othello was voluntary. In the meantime, Othello tells how he met Desdemona and how they fell in love. The duke is impressed with this story, saying that he thought Othello's tale would win his daughter too. When Desdemona arrives, she confirms Othello's story and states that her duty now lies with Othello.
Brabantio withdraws his objection to the marriage; the duke and Othello agree that Desdemona will accompany him to Cyprus where the Turks are supposedly moving to attack. To Brabantio,the Duke declares that Othello is "far more fair than black," giving his approval of Othello and the marriage.
The Duke is approached by Brabantio regarding his daughter being 'stol'n'. The Duke is firm in his support of Brabantio in the injustice of a union without his consent. He says-
Whoe'er he be that in this foul proceeding
Hath thus beguiled your daughter of herself
And you of her, the bloody book of law
You shall yourself read in the bitter letter
After your own sense.
He tells Brabantio that there will be firm justice as he would expect.
However, when the new groom is revealed to be 'valiant Othello', the Duke is prepared to listen to the testimony of Othello and Desdemona. After their lyrical and heartwarming appeals, the Duke's view softens
I think this tale would win my daughter too.
Take up this mangled matter at the best:
The Duke thus tells Brabantio that he will have to make the best of the marriage, as he is as beguiled by Othello's words as Desdemona was. Also, he requires a happy general to lead the fight against the Turks, the duke sees the value in keeping Othello content.