/usr/lib/x86_64-linux-gnu/libavahi-qt4.so is in libavahi-qt4-dev 0.6.32~rc+dfsg-1ubuntu2.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libavahi-qt4.so.1.0.2
/usr/lib/x86_64-linux-gnu/libavahi-qt4.so.1.0.2