Yes just don't touch sda6..LOL
When you boot the LiveUSB to install, choose the "Something Else" option.
You will be presented the same gparted screen; from here you can format "/" sda1 if you like... I believe it will format by default during install. .. Same ext4 is fine...
When installing select sda1 as where to install LL, set the flag?
label? as "/" (drop down option) as well as the bootloader (it will be below this portion, or at least not sda6)
It will reuse swap... thou it may format it.
As sda6 is labeled "/mybkp" you shouldn't have any issues reusing this partition from 3.8 to 4.2 (as "/home" could due to the slight differences between versions)...
Oh you will want to copy off anything within "/home" as I am assuming by the screenshot its part of sda1 and will be formatted...
I think that's it.. Although if you can, a back up of sda6 on another disk/elsewhere never hurts, just in case...