Peter begins to speak specifically to women who are wives.
Just as believers are to “Obey every human authority” (1 Peter 2:13) and servants are to “be subject” to their masters (1 Peter 2:18), wives are to submit to their husbands. The words “Obey,” “be subject,” and “submit” translate the same word.
Here “the word” refers to the gospel message. To disobey means that they do not believe. See how you translated a similar phrase in 1 Peter 2:8. AT: “some men do not believe the message about Jesus” (See: rc://en/ta/man/translate/figs-metonymy)
“they may be persuaded to believe in Christ.” This means that the unbelieving husbands will become believers. This can be stated in active form. AT: “they may become believers” (See: rc://en/ta/man/translate/figs-idiom and rc://en/ta/man/translate/figs-activepassive)
“without the wife saying a word.” Here “a word” refers to anything the wife might speak about Jesus. (See: rc://en/ta/man/translate/figs-synecdoche)
The abstract noun “behavior” can be translated with a verb. AT: “they will have seen that you behave sincerely and respectfully” (See: rc://en/ta/man/translate/figs-abstractnouns)
Possible meanings are 1) “your sincere behavior toward them and the way that you honor them” or 2) “your pure behavior toward them and the way that you honor God.”