Wash. Rev. Code § 35.23.830
In a city initially classified as a second-class city prior to January 1, 1993, that retained its second-class city plan of government when the city reorganized as a noncharter code city, the mayor shall appoint all the appointive officers of the city subject to confirmation by the city council. If the council refuses to confirm any nomination of the mayor, the mayor shall nominate another person for that office within ten days thereafter, and may continue to so nominate until a nominee is confirmed. If the mayor fails to make another nomination for the same office within ten days after the rejection of a nominee, the city council shall elect a suitable person to fill the office during the term. The affirmative vote of not less than seven councilmembers is necessary to confirm any nomination made by the mayor.
RCW 35.23.830