Looking at the orientation of each figure, first we need a reflection over the y-axis, this way the orientation of ABCD will match the orientation of EHGF.
After this reflection, the position of each point will be:
(To find the position after a reflection over the y-axis, we need to switch the signal of the x-coordinates)
[tex]\begin{gathered} A^{\prime}(5,2)\\ \\ B^{\prime}(3,4)\\ \\ C^{\prime}(2,4)\\ \\ D^{\prime}(1,2)\\ \end{gathered}[/tex]
Now, let's write the coordinates of EHGF:
[tex]\begin{gathered} E(1,-2)\\ \\ H(-1,0)\\ \\ G(-2,0)\\ \\ F(-3,-2) \end{gathered}[/tex]
Comparing each corresponding pair of points, we can see that in order to map A'B'C'D' into EHGF, we need to decrease the x-coordinates by 4 units and decrease the y-coordinates by 4 units:
[tex](x,y)\rightarrow(x+(-4),y+(-4))[/tex]
Therefore the answers are y, -4 and -4.
