This scene is set in Padua and Lucientio and Tranio have switched places so that Lucentio can get closer to Bianca the youngest daughter.
In this scene Pertuchio arrives in padua and wants to find a rich wife. Hortensio agrees to introduce him to Katarina so that he can marry Bianca
This is when Katarina and Bianca get in a big fight. After Baptista seperates them Katarina claims that he likes Bianca more. Pertuchio arrives with suitors and Tutors and ask for Katarinas hand in marriage. He agrees
no it is the sun
it is the sun
but thats the moon
fine it is whatever you want
Gremio and Tranio/Lucentio face off to negotiate for Bianca’s hand. Baptista is impressed by Tranio/Lucentio’s promises of enormous riches
This is when Katerina and Pertuchio are getting married and back to where Pertuchio was from where he starves Katerina and makes her wear rags for clothes to get her to listen and do what he wants her to
This is when Pertuchio plays his final mind trick on Katerina by saying the moon is the sun and says they will not continue their journey until she agrees. After this Katarina gives in and gives a speech to all the woman including her younger sister who had been acting out about how to treat a man.