I assume that you have a small room. Apart from whether it is possible from a distance, I would think twice about this projector. 1. it's loud, 2. it's quite a piece of furniture. Both are really noticeable in a small room.
Personally, I also need it in a small room and I'm not really happy with it, partly because I can only get the image small enough by digitally shrinking it and thus losing pixel sharpness.

According to the manual, it can project onto a 150" screen at a distance of 444 to 718cm. So for a distance of 6.5m that should work.
My experience with the projector is that it is so bright (compared to my previous one) that I don't even run it at full power. As a result, it is very quiet and doesn't disturb at all. However, the distance to the screen is only about 4 metres.