[ubuntu] Low Disk Space (again. sigh) Help! in laypersons terms

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http://ubuntuforums.org – I am reeeeeeallly sorry to return to an issue that so many unsophisticated users (like me) have struggled with. I have read the threads that purport to address this Low Disk Space issue but I cannot make heads or tails of the steps they suggest taking. I appear to have run of of space on my "root" (I use terms very cautiously) partition even though I have some 32Gb free on the other Hard Drive. One thread suggested trying a command df -h to see what my disk setup looked like. They then suggested some cleaning steps. Below are the Before view, the steps I took and the After v (Hardware)