Indoctrinate rude hosts in Washington (9)
I believe the answer is:
brainwash
'indoctrinate' is the definition.
(brainwashing is a kind of indoctrinating)
'rude hosts in washington' is the wordplay.
'rude' becomes 'brash' (I can't justify this - if you can you should believe this answer much more).
'hosts' indicates putting letters inside (inserted letters are welcomed or hosted).
'washington' becomes 'wa' (two letter abbreviation for the state).
'in'+'wa'='inwa'
'brash' placed around 'inwa' is 'BRAINWASH'.
Can you help me to learn more?
(Other definitions for brainwash that I've seen before include "Coerce into belief" , "Subject to systematic indoctrination" , "Subject someone to stressful indoctrination" , "Condition" , "clean mind?" .)