When you translate the pre-image point (x,y) right 5 units and up 4 units, we have the image point:
[tex](x,y)\rightarrow(x+5,y+4)[/tex]Therefore, the image point of (4, -6) after a translation right 5 units and up 4 units is:
[tex](4,-6)\rightarrow(4+5,-6+4)=(9,-2)[/tex]The image point is (9, -2)