At Petruchio's home, Katherine complains to Grumio about Petruchio's behavior, telling him she is starved and has not been able to sleep. She begs him to bring her any food. Grumio tempts her by asking if she'd like different kinds of dishes, but he ends up saying that none of them would suit her, and so does not bring any food. Katherine hits him and sends him away angrily.
Grumio exercises a little bit of power over Katherine, teasing her like Petruchio. However, Katherine quickly reminds him of his place when she hits him. She may be a woman, but she is a noblewoman, and he is just a servant.
Petruchio and Hortensio enter. Petruchio has brought a large portion of meat with him, and demands that Katherine thank him for bringing her food. Katherine thanks him, and Petruchio allows her to begin to eat. Petruchio says that he and Katherine will celebrate Bianca's upcoming marriage at her father's house, and he brings in a tailor and a haberdasher with clothes for Katherine. The haberdasher presents a hat, but Petruchio rejects it. Katherine says that it is fine, and that it is the sort of hat gentlewomen wear. Petruchio replies that she can wear one like it when she is gentle.
Petruchio's method of "taming" is humiliating and treats Katherine like a pet animal. She appears to begin to relent, thanking Petruchio for the food he has brought. The clothes that Petruchio has made for Katherine (but then rejects) again show the importance of clothes in a social context. The hat, in particular, signals that its wearer is a noble gentlewoman, as Petruchio jokes that Katherine can wear it when she is gentle.
Katherine protests, telling Petruchio, "I am no child, no babe," (iv.3.79) but he sends the haberdasher off and asks the tailor to show them Katherine's gown. As with the hat, he acts as if the gown is hideous and unacceptable. The tailor says that he made it just as he was ordered to, and Katherine says that she likes the gown. Petruchio acts as if the tailor is insulting Katherine by offering her the gown, and tells him to leave. The tailor reads out the written instructions he was given for the gown, but Petruchio and Grumio still deny that the gown is as they ordered. Petruchio sends the tailor away, but has Hortensio go and tell the tailor that he will be paid tomorrow.
Petruchio continues to act irrationally. He wants Katherine to obey his every word, no matter how wrong or illogical what he says is. At this point, she is still resistant to his control. The gown is such a point of contention precisely because of the social importance of clothing and appearances that has been so emphasized throughout the play.
Petruchio tells Katherine that they will go to her father's in their humble, everyday clothes, minimizing the importance of outward appearances. As they prepare to leave, he says that it is seven o'clock and she corrects him: it is two o'clock. Petruchio tells her, "It shall be what o'clock I say it is," (iv.3.202) and Hortensio marvels at how he orders her around.
In contrast to the importance of clothing and appearances throughout the play, Petruchio insists that such surface-level qualities do not matter as much as someone's true identity and character. He is also beginning to gain some control over Katherine, insisting that she agree with him when he is wrong about the time of day. Note how Hortensio does not care about how Katherine is being treated. He just admires Petruchio's ability to control his wife.