If you are using MBR partitions (instead of GPT partitions), you can only have four primary partitions. If Windows 8 and Fedora already have four primary partitions in use, then there is no place to install Linux Mint except by wiping your hard disk or you manually setting up partitions (which would mean deleting at least one of the four primary partitions, and creating an extended partition in its place--in which you can have as many logical partitions as you want).
It's pretty common for Windows laptops to come with 4 primary partitions in an effort to block installation of Linux, but it sounds like you got yourself in this bind
You can run GParted from the installer DVD / USB to check if indeed you have four primary partitions, and then delete one per your choice. Or if you need help with that, run the following command from the terminal and share the output here. You can copy text to/from the terminal.
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sudo parted -l