I have a second appeal for a secondary school, how can I win it?

I had an appeal for a school place for my child and she failed to get a place but as they made a mistake I've been given a second appeal. How can I make a good case and win it? My main issue is that the school I have been given is over 4 miles away so I'm worried for my childs safety. Has anyone had any experience of this? Any advice or tips? Many thanks