The information on the page is based on the laws of the state of Washington. Landlord-tenant law is very different in different jurisdictions. Even in Washington the information on this website is not a substitute for advice about your circumstances.
A notice to terminate tenancy (a/k/a “20-Day Notice”) is used to terminate a month-to-month periodic tenancy. If the tenant fails to vacate the landlord must bring an eviction action (unlawful detainer action) and follow the exact process as when a tenant fails to cure a 3-Day Notice to Pay Rent or Vacate or a 10-Day Notice to Comply or Vacate.
It is important to understand that the nickname “20-day Notice” can be a bit misleading. This does not mean add twenty days to the current date. The date of termination must be the last day of a rental period. The notice must be served at least twenty days in advance.
Note that in Seattle even for a month-to-month tenant the landlord must have just cause to evict.