"De vrouw zegt hem goedendag."
Translation:The woman tells him good day.
In English you would not write this, you would say "The woman says good day to him"
Both work technically. Itsjust a matter of punctuation 'The woman tells him "Good day"' vs 'The woman says, "Good day" to him' you would not use 'The woman tells, "Good day" to him' though.
Why not "bids him good day"? Might sound a bit old fashioned , but seems the most appropriate translation here, as in German and Dutch you really 'say someone good day', direct dative, and not TO someone.