Hello,
I'm trying to dual boot install Ubuntu Mate from a USB. I have a 2012 Sony Vaio laptop w/ following specs: Core i5, Windows 10, 64-bit, 6 Gb ram. I disabled Fast Restart in windows. When I get to the Mate install screen, I'm not given the "install alongside option."
I've attached a couple screenshots if you'd please take a look. I'd appreciate any guidance as I am a newbie.
~Gabe
You've not mentioned what release of Ubuntu-MATE you're trying to install, but your picture shows four partitions already existing; so if this is a legacy/MBR partition-table you cannot add any more partitions as you've used them all already; thus you cannot 'install alongside' as your partition table is already filled (the legacy/MBR partition table has room for four primary partitions).
Note: Others may be able to recognize these details from the ubiquity installer screen you provided; sorry I can't.
You should then switch to GPT, but doing so with Windows is "difficult", according to Microsoft. My advise is activate UEFI boot, reinstall Windows in EFI mode, then install Ubuntu MATE. You should first save all your information!!! GPT partition table supports up to 128 partitions.
Of course, you should check that the BIOS actually supports UEFI, not all 3rd gen laptops could do that.
My first advice is don't do it.
My second advice is to ask yourself why do you want to do it.
Can a virtual machine be better (you have enough RAM)? Can you afford to put MATE on another physical drive, such as an external drive (you're laptop probably doesn't have a second drive slot but it might)?
Finally, if you still want to do it, I agree with the previous advice to do a clean install.
The above advice is because you say you're a newbie.
I totally agree. I used to dual boot windows, then two Linux OS's and then quit both.
Between Windows policies that do NOT love Linux, UEFI boot and the os-prober being disabled by default, it is no longer safe to your data. There are alternatives. I personally don't use virtual machines, but instead bought a refurbished laptop from an online supplier for a little over a $100 dollars. Over the years I have also gotten used laptops from people that were done with them and going to give them to the salvage people. Good machines, just not the latest and greatest. Again, best advice is find another way.
Thank you! I'll do my best to help.
I appreciate everyone's comments and warm welcome. I've decided to not try and dual boot on my Sony. I'll take the advice to run the live environment then kick out my crappy Windows version when I'm ready to install Linux 
