rsync between two computers on LAN
I am assuming you want to be able to do this both ways, that your username of the logged in user is the same on both machines, that you are happy to get it working as quickly and as simply as possible and that you don't require to use keys to do this.
The steps are:
Set up ssh
You need to install the packages openssh-client
and openssh-server
Then from 192.168.20.9, check you can connect to 192.168.20.10
ssh 192.168.20.10
You will be prompted for the password of your use on 192.168.20.10. Enter that to continue. When asked if it is okay to connect, say yes.
Repeat the process the other way.
rsync
files
To copy a file called todo.txt from your Desktop on 192.168.20.10 to 192.168.20.9, you can do this when logged into 192.168.20.9:
rsync -av 192.168.20.10:Desktop/todo.txt ~/Desktop/todo.txt
Or the other way, when logged into 192.168.20.10:
rsync -av ~/Desktop/todo.txt 192.168.20.9:Desktop/todo.txt
Make it easier.
On machine 192.168.20.9 you can add 192.168.20.10 as a network place in Nautilus under File > Connect to Server and choose ssh and enter your username, password etc. Set this up the other way round on 192.168.102.10. You can then use Nautilus to copy files using scp, ...which is nice.