When people are stressed they have different ways of coping with it. Doctors have identified many different "forms of coping". The sentence you copied mentioned two examples (avoidance and wishful-thinking), and it says that when sociologists found teenagers in the Appalachian area of the United States who used these sorts of coping mechanisms, that they could significantly predict resiliency in those teenagers. In other words, these two coping mechanisms worked and the teens where able to deal with their stress. There are dozens of coping mechanisms. For example, there is "escape" (running away from anything which causes you stress). An Appalachian teen who used escape as a coping mechanism would probably NOT be very resilient in the long run.

It is saying that the teens who coped best in their lives (were resilient) in the Appalachians, were those teens who were both 'wishful thinkers' and at the same time used avoidance strategies (ie. knew how to walk away from problems). ie. Get teens who knew how to avoid/escape negative situations AND who were 'wishful thinkers' (positive ?) then you can predict that these teens were more likely to cope successfully in their lives. I'd need more context to understand what is meant by 'wishful thinkers', but I'm guessing it's those teens who were very positive in how they perceived the world around them.