1. Run Linux.
2. Use console or xterm window.
3. Type commands:
tar -pczf home.tar.gz home/
ls -l home.tar.gz
In result you will see something like:
-rw-r--r-- 1 user group 4000000000 2010-04-09 21:29 home.tar.gz
If the number after user's and group's names and before the date is greater than 4000000000 it isn't possible to store that file on 4 GB USB Flash. If it's less or equal 4000000000 it's possible.
In such case attach USB Flash to your machine, determine the name of the directory where USB Flash is mounted, and copy home.tar.gz file to that directory. I can't be more specific without feedback information.
It isn't necessary to e-mail to LinuxQuestions members when you encounter a problem. The right place for such questions is LinuxQuestions.org forum.