Google calendar doesn't support tasks, only events. So if you try to synchronize a mobile device task in Google, in will lead to an unresolved item since it si impossible to create a task in the calendar. If you want to synchronize tasks, you must synchronize them in a local calendar.
If you want to select in which calendar you want to synchronize the newly created tasks or appointments you created on the mobile device, you must check the option "Link calendar to appointment and task category" in BirdieSync options/Calendar/Category". Then create your appointment or task on the mobile device with the same category name as the Lightning/Sunbird calendar name where you want to synchronize it. You may also set your Lightning/Sunbird calendar as the "Default calendar", so that any appointment or taks newly created on the mobile device which have no category are synchronized in this default calendar. If you want more help, it is suggested to check out BirdieSync help file.