Your L and M partitions are formatted as exFat. I had never heard of it before, but wikipedia tell me it is a proprietary microsoft file system designed for flash drives. Now the L and M drives don't look like flash drives to me, and even if they were, your chances of installing Linux on them would be considerably less than me guessing your favourite colour in one
Strangely enough the only flash drive you seem to have (pendrive) is not formatted in this filesystem. Now maybe you know what you are doing with all this or maybe you don't, but I sure as hell don't know what you are doing, or even how you did it.
I can't see from that pic where linux is installed, L or M, but if it is really installed on one of those on that filesystem I am not surprised it won't boot but I am bloody amazed you got it to install there
You don't have some Mint4Win installation do you?
Anyway, you need to reformat the partition that Linux is on and reinstall it cause it ain't ever going to work on exFat. It should be ext4. Regarding swap, it is not really necessary to have one, but probably best that you do. You have got 8Gb of ram so make it equal to that.
You can reformat using gparted from the live cd or use the installer to do it. The former is probably easier. You know of course that reformatting a partition will wipe any data it contains.
As I am still totally gobsmacked to see what you have done here, I googled a bit more and apparently there is an exfat for linux. This is how to install and use it. Have you really done all this????http://apcmag.com/how-to-enable-exfat-in-ubuntu.htm
And if so Why
Fujitsu Lifebook AH532 Laptop. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Ubuntu12.10 (Unity), Mint14 (Cinnamon), Manjaro (Xfce).