Is it normal that I lost 6 lbs in 28 days then gained 2 lbs back in the following 20 days?
You're talking here about relatively small amounts of weight and relatively short amounts of time. This makes it difficult to distinguish overall reduction in fat, which is your goal, from ordinary fluctuations in weight caused by differing hydration levels and the weight of uneliminated food that's going through your system. For example, I'm someone whose weight has been stable for many years, but my morning scale weight can still vary as much as 4 pounds around its average figure.
All this means that you don't need to obsess over small variations in weight. Track your average weight over time and expect to see minor fluctuations along the way. Also since it's really fat, rather than weight per se, that you're aiming to lose, consider keeping a separate track of your waist and hip measurements. They're actually a better indication of progress towards a healthier body composition. Hip to waist ratio in particular is usually a superior measure to BMI for most people, as it better reflects reduction in visceral fat (i.e. the fat that's deep in the body, not just under the skin). An excess of this kind of fat is particularly hazardous to health, but fortunately it tends to be the first to go in a fat loss programme.
Finally, despite what you'll read about fairly rare metabolic exceptions, weight loss is essentially about calorie balance. Sure, one calorie may not be exactly like another but, in weight management terms, the bottom line is that they're really not that significantly different. After all, common sense should tell us that people have gained and lost weight around the world and throughout history on a huge range of different diets. Furthermore, in the developed world, the rise in average weight has been accompanied step by step by the easy availability of high calorie foods. So it doesn't take a genius or an "expert" to see the connection.
Consequently, some of the variability you've seen may just be due to differences between what you've eaten over those periods and how physically active you've been. You don't need to track calories obsessively, but you do need to maintain a modest deficit over time. It's just a reversal of the process by which you gained weight in the first place. Some people, myself included, use methods like intermittent fasting to help manage weight long-term. It's not the only approach, but it's effective. Google if you're interested.