How do I free up disc space for my 10.6.8 Mac OS X?

I have two external 1T and 2T drives plugged into my iMac 10.6.8. Whenever I try to transfer files from one drive to another my iMac stop working - and I get a a note saying I don't have enough space and should delete files.

These are final cut pro files so they are quite large. I can not upgrade to 10.10 or higher because my version of Final Cut Pro doesn't work with the newest Macbook Pro (which I also have and it kills me that I can't use my laptop with Final Cut).