The 6th house rules health, work, personal habits, and daily routines. It shows how we act in service to others. Saturn in Sagittarius transiting H6 can reveal how ineffective our routines are, or any detrimental personal habits. It can also reveal a health condition, or work issues (perhaps anxiety issues due to the stress of a work situation, for example).
If Saturn is currently transiting your 6th house, then you have Scorpio or Sagittarius on the cusp. Scorpio-cuspers are secretive about their health and work issues, and resistant to change. You may fear losing control by making any adjustments, but Saturn’s presence makes it clear (perhaps through a serious health issue) that changes need to be made. Fortunately, you are naturally good at transformation.
If you have Sagittarius on the 6th house cusp, you seek change naturally, and may frequently switch jobs, or have multiple ones that spread you too thin. You are easy going about your health and may over-indulge in the spirit of fun. Saturn makes it apparent that you need to clean up your personal habits and put in place a routine.
For both of you, this transit is an opportunity to make necessary changes in your work and health routines, including diet, exercise, and stress management. It could possibly lead to a change in vocation, but that’s up to you. You will have to re-define what your beliefs and philosophies are in these areas, and choose realistic options in which to practice them.