There is no need to do push-ups during fat loss, which has no effect on fat loss. Eat less greasy food, chew slowly every meal until you are 60% full. No drinking, no drinking, no snacks. Reducing fat is very simple, and there is no technical work. I can give you a diet if you want. You know, controlling diet is the most fundamental thing to lose fat. Exercise is an auxiliary means. You'd better run before breakfast, on an empty stomach or before dinner. Solid ball is a skill exercise, which has no effect on increasing muscle or reducing fat.
Then you said that building muscles requires heavy and special training. What you have in the picture is far from a few push-ups. I suggest a gym, or at least barbells and dumbbells. Really not good. You can buy a set of dumbbells to practice at home, and it can also produce some effects. Of course, it's definitely not as good as a photo.