We have to find the transformation that will have an image that is all in the first quadrant.
We will see one by one:
1) Translation 4 units to the right: for the point S it will not place it in the first quadrant (it will fall in the second quadrant), so it is not right.
2) Reflection acroos the axis x=4. Points Q and R stay in the same place, P falls in the first quadrant but S falls in the second quadrant. Not enough.
3) Reflection across y=-x. This is refelction across a diagonal axis. Point Q will fall in the opposite quadrant (3rd quadrant), so it is not the rigth transformation.
4) Rotation 90 degrees counterclockwise over the vertex Q. All four points, when rotated from the vertex Q, 90 degrees counterclockwise, falls in the first quadrant.
5) Reflection across x=3 and translating 8 units up. The reflection will get all the points in the first and second quadrant. When translated 8 units up, all points fall in the first quadrant.
6) Reflection across the x-axis and translating 13 units up. When reflected across the horizontal axis, P falls in the 3rd quadrant. If it is not translated to the right besides up, it won't be in the 1st quadrant. So this transformation is not the correct one.
The transformation that gives an image with the four point in the 1st quadrant are 4 and 5.