Why is my Mac's Flash Storage full?

Question

I have an issue on my Mac where my flash storage's free space suddenly shrank.
            I am using a Macbook Air (128 GB). As the storage is pretty small, I am trying to keep my storage as efficient as possible. Last 3 days, my free space is 37 GB.The next day, I am given a task to edit a large video, from multiple devices which i copied to my desktop. After hours of editing on Final Cut Pro x, the movie is done, but when i rendered the video and i looked at my storage's free space, the space has shrunk to 4 GB.
               I have a portable hard disk, which i used to store large-sized data, and i managed to move all those storage-eating files. After moving, i then delete the original file on the desktop to the trash, then i emptied the trash. I looked at the 'About my Mac' to the storage tab, the free space has increased from 4 GB to 8 GB. Where is my previous 37 GB free space? 
               I have tried to: - Move the media used for the large video-editing to another Hard Disk
                                         - Deleting iPhoto's trash
                                         - Move all downloads files to another Hard Disk    
                                         - Emptying Trash
                                         - Emptying 'Mail' trash
                                         - Clearing desktop folders
                                          - Clearing Final Cut Pro's media library
My question is, where is my previous free space? Does Final Cut Pro's Library takes up Storage Space? Should i delete the 'Project' folders on Final Cut Pro? What should i do to get my free space?  Thank you..
System: Macbook Air (13")                                  System Software: Final Cut Pro X (v10.1.2)
               [128GB]                                                                                 OSX Mavericks 10.9.4
               i5 Processor
               Intel HD Graphics 5000
               4 GB RAM

Answer 1

Of course the library takes up storage space.
Freeing Up Space on The Hard Drive
  1. See Lion/Mountain Lion/Mavericks' Storage Display.
  2. You can remove data from your Home folder except for the /Home/Library/ folder.
  3. Visit The XLab FAQs and read the FAQ on freeing up space on your hard drive.
  4. Also see Freeing space on your Mac OS X startup disk.
  5. See Where did my Disk Space go?.
  6. See The Storage Display.
You must Empty the Trash in order to recover the space they occupied on the hard drive.
You should consider replacing the drive with a larger one. Check out OWC for drives, tutorials, and toolkits.
Try using OmniDiskSweeper 1.8 or GrandPerspective to search your drive for large files and where they are located.