The diets in this study were designed, controlled diets (e.g. the meals were handed out, not left in the hands of the study subjects) so calorie levels and nutrition values were equivalent among subjects. Individual variations in metabolism were also accounted for as everyone did all the diets, in a random order. Low carb still burned 300 calories more per day than low fat. It's true, the study only comprised 21 people in a metabolically deranged subset of the population (obese teenagers); that would also explain higher systemic inflammation during low carb (fat burning in obese individuals can release fat-soluble toxins into the blood to be excreted, which is why fat loss sometimes makes you feel physically miserable), (not to mention that teens are an inflamed bunch in general, what with all the hormonal block parties going on in them). In the end though, they didn't have an explanation as to why low carb burned more calories than low fat, only that it happened. 300 calories a day is still a significant number though, and worth looking into.
1) eat real food - more vegetables, moderate meat, moderate fruits, less grains, less sugar, less vegetable oils.
2) exercise - moderate intensity cardio, sprinting, heavy lifting, dedicated stretching and mobility.
3) live - relax, de-stress, meditate.
Disclaimer: I'm not professionally qualified to make any formal recommendations. I've just done my homework and I'm my own guinea pig. All of my data, unless otherwise cited, comes from a sample size of n=1 (me).