I wouldn't be able to give examples because Jesus did not elaborate on what "this kind" means. I'm guessing it would be the stubborn issues in our lives in which we just can't seem to get breakthroughs. I love to read spiritual fasting testimonies about people getting breakthroughs via fasting and prayer. Fasting and prayer has changed people's destinies. In my own life, even with the small amount that I have done, I have noticed that it is much easier to get my prayers answered. I am far from attaining what I need to with fasting and prayer.