[CentOS] need to free space on a root partition.

Hello, there,   Happy new year everyone!
    I am puzzled here. Could some expert help me shed some light on  
this?
this may not be a centos specific Q..
i have a linux machine. and the root partition (/) is full..
so I moved a dir from /data to /var (/var is on a different  
partition), and created a link from /data/fa to /var/xyz, the files  
under /var/xyz is about 8G,
du  /var/fa
8701248 /var/fa

so I thought this should free some space for me, but when I used df,  
it gave me similar results before and after the move..   and my rpm  
installation would fail due to the lack of space..

Filesystem           1K-blocks      Used Available Use% Mounted on
/dev/cciss/c0d0p6     15235040  15232452         0 100% /
/dev/cciss/c0d0p8    other partitions have free space....

I was confused on why moving a 8G file to another partition did not  
free some space for me?
and I did see that the disk usage for the destination partition/disk  
increases after the move..

any pointer is appreciated!
yan