It’s definitely possible, though it is also a good idea to speak to your doctor if you want to try and lose so much weight so quickly. A generally accepted goal of losing 0.5kg to 1kg per week is usually considered ok, and for this you usually need to burn 500 to 1,000 calories more than you consume each day, through a lower calorie diet and regular physical activity.
So if you aim to lose 20 kg, you should be able to accomplish this in around 20 weeks. But it is not easy-90% of the work here is going to be done in your diet and what you eat.
To be honest, to some degree it doesn’t matter what kind of diet you are on-if you are on a high fat diet taking in more calories than you burn you will put on weight just as if you were on a high carb diet. The key is to be in a caloric deficit. It is important to bear in mind that diets high in fat tend to have a much higher caloric density than foods low in fat.
I find personally, a high carb low fat ( generally 75-80% carbs) plant based diet the best way for me to lose weight on a sustainable basis. I find this helps me to very easily be in a sustained calorie deficit.
If you are not seeing any change in your bodyweight you are eating too many calories and not moving enough.
If you haven’t already check out the below for some inspiration 
