Solaris

clear up any log files at /var/adm
u can zip them and empty logs by using the ">" command
also ... you can remove the core files using :

"find / -name core -exec rm -f {} \"

...high chances...this will reduce the treshold...good luck

An earlier df -k shows that this system does not have separate /usr, etc. slices, running:
# cd /
# du -sk ./* | sort -n
will show which sub-directory of root contains the the most files, you may then CD into it and repeat, looking for core files, large archive files (either tar, zip, etc.) that may be moved off the system without breaking it.

I am sending the output of /usr,/var and /opt

# df -k /usr
Filesystem kbytes used avail capacity Mounted on
/dev/dsk/c0t0d0s0 2148263 1733247 372051 83% /

# df -k /var
Filesystem kbytes used avail capacity Mounted on
/dev/dsk/c0t0d0s0 2148263 1733247 372051 83% /

# df -k /opt
Filesystem kbytes used avail capacity Mounted on
/dev/dsk/c0t0d0s0 2148263 1733247 372051 83% /


now what i have to do to solve this problem

You're in the best position to know what to remove or not than any of us here dude..
Under /var,
check the /var/crash/`hostname`, remove or save the core files (if any to tape of disk if you need it.

under /var/tmp
remove all the unnecessary or unneeded files, usually ppl would unpack the patches in there before applying patch to the system. If the patches is already installed, removed the whole /var/tmp/9 or /var/tmp/10/ dir (based on your OS version)

under /var/adm
check all the messages file. messages is the latest followed my messages.0 , messages.1 and so on.. Tar/zip up the old logs in there..

under /opt,
check if unwanted packages are in there uncompressed .. If the package is already installed in the system, you might back it up somewhere.. again the same..
under /usr .. usually I wont touch anything there first..

there will be huge logs at /var/adm and /var/logs

lastlog and wtmpx at /var/adm

syslog at /var/logs

compress those logs...