Petruchio and Hortensio continue their light hearted banter. Picking up on Petruchio’s phrase “put her down,” Hortensio replies with a sexual innuendo: it’s his job (office) to put the widow down, i.e. get her into bed. Petruchio extends the innuendo while punning on “office”: Hortensio sounds like a police officer enforcing a husband’s marital rights.