Have a look at the search input lineedit in Marble (in the main toolbar. you might have to make it visible first): On its left it shows a search icon and a dropdown indicator. Clicking on the icon opens a menu.

In this task the same type of interaction should be implemented for the routing input widgets (in the routing tab). Currently it is separated into a push button that opens a drop down menu and a line edit. Merge both in the same style as the search lineedit.

Have a look at SearchInputWidget and MarbleLineEdit to understand how the search lineedit is implemented. Then transfer it to RoutingInputWidget.cpp.