$ sudo apt-get update
$ sudo apt-get install openjdk-6-jre-zero 

openjdk-6-jre-zero is installed in your system.

Make ensure the openjdk-6-jre-zero package were installed using the commands given below,

$ sudo dpkg-query -l | grep openjdk-6-jre-zero *

You will get with openjdk-6-jre-zero package name, version, architecture and description in a table

openjdk-6-jre-zero package basic information: