In the tutorial, it shows how to setup Root, Home and Swap partitions. In your case (since you've got limited space for Mint), it's best to just use a Root and Swap partition. That's what is already on the drive right now, so you only need to point the installer to use them.
- Boot Mint disk and start installer
- Choose "Something else" install option, which will bring you to partition selection page
- Do Not tell installer to create a new partition table. That would wipe out your Windows installation.
- Highlight /dev/sda6, click the "Change" button
- Use as = Ext4 file system (or similar wording)
- Size = leave as is already filled-in
- Mount Point = "/" (for Root)
- Check box to format the partition
- "Apply"
- If you get a message complaining that you changed the size of partition (even though you did not), ignore it and hit the "Back" option of the message. All will be fine -- it's just a weird quirk of the installer program.
- No need to do anything with the Swap partition. The installer will automatically use it for the install.
- IMPORTANT: Near bottom of window, make sure "Device for boot loader installation" is set to /dev/sda (not /dev/sda6).
- Click to "Finish install" when done with above.
- Shutdown/Reboot when install finishes. (Don't forget to remove install DVD/USB after shutdown, but before it reboots. Otherwise you may end up booting back into live Mint instead of new install on HDD.)