First call the Windows API function FindWindow() to retrieve the handle to the TaskBar Window, then call the Windows API function ShowWindow() passing the predefined constant SW_HIDE. Example:

procedure TForm .Button Click(Sender: TObject);
var
  hTaskBar : THandle;
begin
  hTaskbar := FindWindow('Shell_TrayWnd', Nil);
  ShowWindow(hTaskBar, SW_HIDE);
end;
procedure TForm .Button2Click(Sender: TObject);
var
  hTaskBar : THandle;
begin
  hTaskbar := FindWindow('Shell_TrayWnd', Nil);
  ShowWindow(hTaskBar, SW_SHOWNORMAL);
end;