{With SHAppBarMessage }

uses
ShellAPI;

procedure TForm1.Button1Click(Sender: TObject);
var
tabd: TAppBarData;
PosString: string;
begin
FillChar(tabd, SizeOf(TAppBarData), 0);
tabd.cbSize := SizeOf(TAppBarData);
if SHAppBarMessage(ABM_GETTASKBARPOS, Tabd) = 0 then Exit;
with Tabd.rc do
PosString := Format(' (%d, %d);(%d, %d) ', [Left, Top, Right, Bottom]);
case tabd.uEdge of
ABE_LEFT: ShowMessage('Left Position' + PosString);
ABE_TOP: ShowMessage('Top Position' + PosString);
ABE_RIGHT: ShowMessage('Right Position' + PosString);
ABE_BOTTOM: ShowMessage('Bottom Position' + PosString);
end;
end;