Can anyone tell us how to program a logic that can move gamestones on this field.
Nobody here is going to program your game for you. As ra4king says here:
http://www.java-gaming.org/topics/hello/24411/msg/205121/view.html#msg205121, We are here to guide and point you, not write your code for you.
a logic that can move gamestones on this field but for different Displaysizes.
What is your question? Do you want to move objects around on the screen? If so, how are you drawing those objects? Do you want to draw a grid on the screen? If so, do you want the grid to have the same amount of cells in the x and y direction, regardless of screen size, or do you want them to be the same size apart, on any screen? Please clarify your question. No one has helped you yet, because no one knows what your question is.