I think whether or not you finish things or not (I guess you are talking about goals, projects, work etc) would be more about the signs that your planets are in and not really the houses. I could see the 6th and 10th being more related to work type of projects.
I think when you have empty houses it means that those areas of your life (for this, 3rd house is communcations, 6th is House of Service and 9th House is hte house of Long Journeys [foreign travel etc]) it just means that, in your life, you do not focus as much in those areas as you do in others. Not that they don't have a place in your life not as much importance is placed.
If you have a planet in those houses, than I believe you should be looking at the signs those planets are in. For example, Virgo is a signs that finishes things and can't leave them unfinished. The signs is the "how" you carry out the personality of that planet. YOur houses are just telling you where in life that is carried out.
So if you have no planets in those houses, I wouldn't imagine many unfinished or even things started in those areas of life. Maybe this why it looks like that you are not "finishing" things. It is just that these areas in you life don't have as much emphasis as other areas.
That said, my 3rd house is empty, one planet (Saturn in Taurus) in my 6th house and one planet (venus in leo) in my 9th. And I always finish things - granted I may have several projects going on at once and a may put one on hold for various reason or another but they always get finished. I can't leave things unfinished - the concept is alien to me.
But I think you might want to take a closer look at the signs to explain why.