For me, the handle is a really important part of any bat and not often talked about other than in shape. I hear people saying they love a whippy handle, but imo a slightly stiffer handle is preferable for power and longevity.
I see a lot of rehandles, largely due to poor quality handles which have a lot of whip/flex and you can see the cracks starting from the handle inserts, going down into the neck and into the shoulders.
A good quality handle for me has some flex, but not excessive twist or flex. It just causes issues all round imo.
4, 6 or 12 piece are obviously the amount of seperate pieces laminated together to make the handle. Depending on who you speak to depends on the pro's and cons of each. Even though they're more expensive, i now only use 12 piece as i prefer them and feel that have the right level of flex/stiffness/longevity for me. I use them in all of my bats regardless of Grade, as prefered then to the 4 piece ones i used.