unit Unit1;

interface

uses
  Winapi.Windows, Winapi.Messages, System.SysUtils, System.Variants, System.Classes, Vcl.Graphics,
  Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.ExtCtrls, Jpeg;

type
  TForm1 = class(TForm)
    imgPos1: TImage;
    imgPos2: TImage;
    imgPos3: TImage;
    imgPos4: TImage;
    imgPos5: TImage;
    imgPos6: TImage;
    procedure FormShow(Sender: TObject);
    procedure imgPos1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;
  lastClickedMovableImage: TImage; {hold the component that was clicked}

  imgNameArray: Tarray<string>; {array to know which image is in which component}

  const aImageFileName = 'E:\Delphi Projects\MoveImage\A.jpg';
  const whiteImageFileName = 'E:\Delphi Projects\MoveImage\white.jpg';
implementation

{$R *.dfm}

procedure TForm1.FormShow(Sender: TObject);
var
  appPath: String;
  posImg: TImage;
  pos: Integer;
  imgPosName: String;

begin
  {you'll need this to point to the EXE path after the project is compiled
   to point to the image files included with the EXE}
  appPath := ExtractFileDir(Application.ExeName);

  {set the initial position images}
  for pos := 1 to 6 do
    begin
      {find each TImage component on the form}
      imgPosName := Concat('imgPos', pos.ToString());
      posImg := TImage(FindComponent(imgPosName));

      if (pos = 1) then
        begin {default position 1 as teh starting position for the image that will move}
          posImg.Picture.LoadFromFile(aImageFileName);
        end
      else
        begin
          posImg.Picture.LoadFromFile(whiteImageFileName);
          posImg.OnClick := imgPos1.OnClick;  {assign all other TImage components the same event handler}
        end;

    end;

    imgNameArray :=  TArray<string>.Create('A','white','white','white','white','white');
end;

procedure TForm1.imgPos1Click(Sender: TObject);
var
  imgName: String;
  clickedImg: TImage;
  imgPos : Integer;

begin

  imgName := TImage(Sender).Name;   {component name which contians its position on the form}
  imgPos := StrToInt(imgName.Substring(6));

  clickedImg := TImage(Sender);

  {what image is in this clicked TImage component}
  if imgNameArray[imgPos - 1] = 'A' then
    begin
      {this image can be moved}
      lastClickedMovableImage := clickedImg {remember this image}

    end
  else
    begin
      if lastClickedMovableImage <> nil then
        {a white space was clicked and there was a value in lastClickedImage
         meaning it was the image that can be moved}
        begin
          {move the A image from it's current location to the last clicked
           white space}
          clickedImg.Picture.LoadFromFile(aImageFileName);

          imgNameArray[imgPos - 1] := 'A';

          {put a white image in the previous location of the moveable image}
          lastClickedMovableImage.Picture.LoadFromFile(whiteImageFileName);

          imgName := lastClickedMovableImage.Name;
          imgPos := StrToInt(imgName.Substring(6));
          imgNameArray[imgPos - 1] := 'white';

          lastClickedMovableImage := nil;
        end;
    end;
end;

end.