The given point is:
[tex]A(-5,4)[/tex]From the graph, when you move 6 units to the right, you add 6 to the x-coordinate of the point and when you move 2 units down, you subtract 2 units from the y-coordinate:
[tex]\begin{gathered} A^{\prime}(-5+6,4-2) \\ =A^{\prime}(1,2) \end{gathered}[/tex]Therefore, option D is the correct option.