Jamal,
The Help says that the Input database connection defaults "to use the workspace defined in the environment".
Since I already see the versions filled out in the dialog, I don't think there is any need to fill in the "Input database connection", as it probably just uses the connection information from the context from which you opened the option (in your case I guess the Geodatabase Administration dialog).
I think the "Input database connection" text line is just an "extra" available for when you use the Reconcile Versions option straight from ArcToolbox, in a ModelBuilder model, or in Python scripting, when the connection isn't yet defined. It would have been better if unnecessary options were hidden in specific cases like this, but I guess this is the small price we need to pay for something like the flexible ModelBuilder and ArcToolbox framework.