The most stable conformation of 1,2-dibromoethane is:

I have attached an image that shows the most stable conformation of 1,2-dibromoethane. The top image shows the line drawing of the structure and the bottom image shows the Newman project of the structure. The Newman project shows up the perspective of looking down the C1-C2 bond of the compound. From this perspective, we can see the relationship between the two bromo-substituents.

Since the bromo-substituents are the largest groups substituted on each carbon atom, these groups will want to be as far away from each other in space as possible. The result is this anti- relationship shown, where the two bromo atoms are as far away from each other as possible within the molecule to reduce the amount of steric interactions. Therefore, the anti-conformation is the most stable conformation of 1,2-dibromoethane.