Ok, let me see if I can understand what you are asking/saying.
You boot up into "rescue" mode on a installation CD. Then, you mount your root partition of a linux install. You then chroot, which changes your root directory to /dev/sda6 instead of the virtual root that your install CD has created. You then want to access /dev/sda8 to copy a file to it. df, mount or any other tool you use will likely be incorrect in this environment. /proc is created from the install CD, therefore when you chroot, the /proc that NOW exists is empty, and your tools that cat info out of the proc filesystem will report this information incorrect because of this.
If you just want to copy a file from /dev/sda6 to /dev/sda8 then you can mount them and copy files without having to chroot into your /dev/sda6 filesystem.
mount /dev/sda6 /mnt/sda6
mount /dev/sda8 /mnt/sda8
Then to copy a file:
cp /mnt/sda6/file /mnt/sda8/file
If there are subdirectories involved you can list them just the same. So, for sake of example, we'll use /var/log/messages We are going to assume you want to copy /var/log/messages to your fat32 partition, just in the root of the partition (listed in windows as something like C:\)
so to do this, we mount the devices as noted above, then:
cp /mnt/sda6/var/log/messages /mnt/sda8/
And it will copy the messages file to the fat32 partition.
If I misunderstood your question, feel free to clarify.