Most likely, you should update the existing GRUB boot loader.
The existing GRUB boot loader may have been installed to
/dev/sda6 or, likely
/dev/sda3 biosgrub 9 MB? Anyway, I am guessing that your first Linux distribution was Ubuntu.
Therefore, do the following steps.
Step 1: Boot and login to Ubuntu 14.04 (or your first Linux distro)
Step 2: Open Terminal, and run
sudo update-grub command; You should see some output with list of Linux distributions found on each partitions
Step 3: When finished, close the Terminal and reboot your machine.
Now enter into GRUB boot menu again and you should be able to see Elementary Freya being listed together with Ubuntu 14.04.
Comments to your questions
So is there any way I can fix this? Or just try reinstalling Elementary? Please tell me with details which partitions I should choose.
Reinstallation may be risky, since you multi-boot with Windows. Not sure how far Windows-Linux coexistence had improved since XP, but I had more failures than successes back then. Regarding my experience of failures, you may read Side notes at bottom.
As you can see, /dev/sda8 was formatted; it's where Freya was installed. By the way, do I need to define another swap partition for Elementary? Or it will use the same one Ubuntu does?
The installation is most likely default, since there is only one partition being mentioned by you.
By default, Elementary (or Ubuntu) will auto-detect your amount of main memory or RAM and set up the SWAP size by itself. It's automatically set up by the installer so you can forget about it.
For advanced installation, choosing "Something else" option in the installer will allow you to set the amount of
/home on different partitions. If you don't know what are these, you can just ignore (This will pull another long answer, or you can just google this out).
For the "boot loader installation device location" I chose
/dev/sda8. Maybe this is the problem: I chose that instead of just
No, your made a good decision here.
For a machine having multiple Linux distributions on the same hard disk, the boot loader should be installed to the same partition where the new Linux distribution would be installed (or don't install the new boot loader). Then, always use the existing boot loader.
The existing boot loader, GRUB, is the default boot loader for Ubuntu. So if you had installed any Linux distribution after that, boot into Ubuntu and run
sudo update-grub to tell GRUB of the changes made to the hard disk.
If, let's say, Elementary Freya is the only operating system on the hard disk of your machine (and no other Linux, Windows or Mac), then you should be choosing
I say "any" boot menu because there are two: first the one for Windows 8 pops up, with this OS as its only option, and if you press Esc, GRUB pops up, with Ubuntu, elementary OS Luna and two more options.
In your case, you have two bootloaders: Windows boot loader and GRUB. It seems that your Windows boot loader is chainloading the GRUB boot loader.
On second thought, I see like this: Windows boot loader being the first to be loaded, but when escaped, it falls back to GRUB boot loader being the second in line. Those two boot loaders may be loaded sequentially by the BIOS, although I'm not sure if this possible (ask someone else for this).
In fact, it is possible to use Windows boot loader to detect Linux distribution which has been explained here and there (See Disclaimer at most bottom).
Or in the other way I can look at it, if I had chosen
/dev/sda instead that means it will create a partition for the boot loader and no problem.
/dev/sda means that the boot loader will be installed to Master Boot Record (MBR), the first sector of a hard disk. It won't create any additional partition.
So if you view the partitions in a partition editor such as GParted or Gnome Disk Utility, you won't find any other partiton than
/ (root) for a default, single Linux distro installation.
My worst experience was when I set up dual-boot Windows XP and Ubuntu on two different laptops with different hardware configuration. I "successfully" bricked (permanently damaged) Wi-Fi adapter card, twice. Both machines. Since then, I vow to never dual-boot with Windows again.
I quote the links to prove the possiblilties of using Windows boot loader (and without using GRUB at all), but not for recommendation. After all, your existing set up is working well regardless of how you did it. There is no reason to change the set up, unless updating GRUB didn't work for you.