No, you cannot delete a Facebook account without knowing the password. Facebook accounts are protected and encrypted with passwords for security reasons. Therefore, if you want to delete your account, you will need to provide the correct password in order for it to be deleted. If you have forgotten or lost your password, there are several options available to retrieve it; such as requesting a reset link via email or answering some security questions. However, if these options do not work out then unfortunately it is impossible to delete an account without knowing the password.