public DockPaneState DockState {get;}

{
  // in order to find a dockpane you need to know its DAML id
  pane = FrameworkApplication.DockPaneManager.Find(dockPaneID);

  // determine visibility
  bool visible = pane.IsVisible;

  // activate it
  pane.Activate();

  // determine dockpane state
  DockPaneState state = pane.DockState;

  // pin it
  pane.Pin();

  // hide it
  pane.Hide();
}