Well,
If two images are similar, then the ratios of their respective sides must be equal. So is EF is 2 units long and E'F' is 6 units long, and the images are similar, we can use this info to determine the ratio of the preimage to the dilated image. We obviously know that E'F' is bigger, per the attachment.
6 = 3(2)
Therefore, E'F' is 3 times as long as EF, and that makes image D'E'F'G' larger by a scale factor (ratio) of 3.
The correct option is D.