You can use a scale factor of 2 to dilate the original and get the final. I got this answer by doing:
y x 6 = 6y (y represents the original rectangle, 6y represents the second rectangle)
then, 6y x 1/3 = 2y (2y represents the final rectangle)
If you compare the original rectangle (y) to the final (2y), you see that the final is 2 times the original, therefore the scale factor is 2