There are three steps to this process
Step One: Make your brother a member of your group.
Your group-name is same as your user-id. Say, if your user-ID is
akumar your group name is also
akumar. If your brother's ID is
bkumar, then you want to make
bkumar a member of the group
akumar. See How to manage users and groups? for how to add your brother's user-ID to your group.
Step Two: Change the permission of the folder you want to share.
Open Nautilus. Right click on the folder you want to share. Go to permissions tab. look for the group permissions and change it into "Read and Write." Check the box for allowing the same permissions to the files and folders inside.
Step Three: Verify that your brother can create delete files in the shared folder.
Let your brother login to the computer. Open Nautilus. It will open to your brother's home folder. Navigate to your home folder and open the shared folder by:
click on Computer or System Files (depends on the version of Ubuntu) on the left panel.
Double click on home folder, double click on folder named akumar inside home.
Create a file in the folder. Delete the new file.
Step Four: (optional) Make a link of this folder to your brother's home folder.
while logged in as your brother, open another window of Nautilus next to the first one, by middle-click or Ctrl+Left click. In your own home folder where the shared folder resides, hold down Ctrl+Shift and drag the shared folder to your brother's home folder.
Hope this helps