Based on how you're describing, I like the two rows, 3x2. This is just a personal preference thing tho. I wouldn't split them on two dimmers. I can't imagine wanting to set half the can lights on one dim level and half on another. I'd put them on one dimmer, then wire the 2nd dimmer to a couple floor half-outlets or accent lighting. Then you can run the can lights or the other lights (floor lamp) or both.

I would also put them slightly farther apart than even spacing wall-light-light-wall. Otherwise it will be overly bright down the center where their beams overlap and not as bright on the fringe. With 13', I'd go something like 3.5' light to wall on each side with 6' between the two rows. That's just what I'd do.

Thank you very much for your help, squishyball. I did not consider the light beam overlap at the center.

Can I have the layout as follows.

Parallel to the 13' wall, 3.5' (wall to light; the side where sofa and piano are placed in living room, and where two computers are placed in family room), 5' (inter-light distance), 4.5'( light to wall, less traffic side). It's not symmetrical, but I don't know if it would be fine.
Paralell to the 16' wall, the distance to wall and inter-lights distance would be: 3', 4', 4', 3'.
6 (2 by 3) lights of 800 lumens Cree CR6 LED recessed lights in all in each room.

Really appreciate your help.

2 rows of 3 lights each ~ 3' to 3.5' from the walls (depending on the location of the ceiling joists) would be great.

The center of the room does not need to be as well lit as the sides as furniture is typically placed alongside the walls while the center is left open for mobility.

The number of dimmer switches really depends on how you envisage using the room. For example - only the piano could be lit while the rest of the room is not.

Thank you very much for your help, David.