The password you should give when the sudo
command is executed is the password of your account, not the root
password. Try with your personal account password and let's see how it goes.
If it still fails keep reading my answer.
During your fedora installation you probably did not flag the check box to add your personal account to the administrator group (which by the way in fedora is the wheel group).
You should still be able to become root running the
su -
command if you know the root password, which I am assuming you do.
One of the ways to fix your problem is to add your personal account to the wheel group running (as root) the following command:
gpasswd -a username wheel
At this point retrying
sudo yum install java-1.0.6-opendjdk-devel
will only prompt for your personal account password and will run with no further issues or warnings.