How to revert to older version of libc6 in Ubuntu?

The biggest problem is likely going to be to find the exact version that you had installed before as a .deb, especially if you did apt-get autoclean in between.

In general to install a particular version you would do

sudo apt-get install libc6=2.13-20ubuntu5.1

then you could mark the package as held using:

echo "libc6 hold"|sudo dpkg --set-selections

so that subsequent updates don't update it automatically. Problem for you would be to find a mirror that has the old version and use that or find the .deb for the old version and use dpkg -i ... to install it manually.

Try locate libc6_2.13-20ubuntu5.1_amd64.deb to see whether you have a cached copy.

However, what are the symptoms of the failing program? It's possible there are solutions to the problem other than reverting to an older version of libc6.