There are several settings and restrictions of privacy of created tasks.
Prohibition of Private Tasks Creation
One can add the special line that disables the creation of private tasks to the teamwox.cfg configuration file, located in the /config directory of the TeamWox installation folder:
Once that line is added and the TeamWox system is restarted, the button, that allows assigning the privacy status, will disappear from the window of task creating. Thus the tasks will be available to the members of superior departments, that have the "View tasks of employees of subordinate departments" permission, and to the employees allowed to view the tasks of the group.