How do i stretch an image like this in a video on sony vegas pro 13?
First off, welcome! I would like to state that in the future you should make you questions a bit more detailed.

From what I understand you either want to (1) stretch the image to remove the black bars, or to (2) scale the image.

Either can be done by dragging the clip on to the timeline and hitting the pan/crop button on the clip (it looks like a box, not the plus sign).

From there you will find a window where you can scale the clip according to the aspect ratio. If it does not conform to the 16:9 aspect ratio or the 4:3 ratio you want you can select one of those ratios from the drop down and scale the clip to remove the black bars. If you want, you can also disable the the current ratio with one of the buttons on the side of the window. From there you can adjust the image freely without an aspect ratio limitation. Bare in mind, This can cause undesired effects such as squeezing the image in either direction.