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ImageY.Left := 500;
ImageY.Top := 200;

ImageX.Left := 600:
ImageX.Top := 150;					

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procedure TForm1.Image1Click(Sender: TObject);
var oldx,oldy:integer;
begin
oldx:=image2.Left;
oldy:=image2.Top;
image2.Left:=image1.Left;
image2.Top:=image1.Top;

image1.Left:=oldx;
image1.Top:=oldy;
end;					

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procedure TForm1.Image2Click(Sender: TObject);
var oldx,oldy:integer;
begin
oldx:=image2.Left;
oldy:=image2.Top;
image2.Left:=image1.Left;
image2.Top:=image1.Top;

image1.Left:=oldx;
image1.Top:=oldy;
end;					

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Image := TImage(FindComponent('Image'+IntToStr(i)));
if (Image.Left = 150) and (Image.Top = 500) then
  begin
    // Image.Left und Image.Top verändern
  end;					

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var a: Boolean;
    old: TImage;

[...]

procedure TForm1.Image9Click(Sender: TObject);
var i, oldx, oldy: Integer;
begin
  oldx:=image9.left;
  oldy:=image9.top;
  if a=false then
    begin
      image9.Left:=616;
      image9.top:=160;
      a:=true;
    end 
  else 
  if a=true then
    begin
      for i:=1 to 45 do
        begin
          old := TImage(FindComponent('Image'+IntToStr(i)));
          if (old.Left = 616) and (old.Top = 160) then
            begin
              old.top:=oldx;
              old.left:=oldy;
              image9.Left:=616;
              image9.top:=160;
            end;
        end;
    end;
end;