How much calories should a 8 year old eat per day?

Unless your 4 year old is considerably overweight, you should not be putting a calorie restriction on them at that age. If your child is very overweight then you should consult your pediatrician to formulate a diet for the child.

Children's bodies are not miniature version of adult bodies and need different requirements. At that age, the myelination of their nervous system is not complete, and the main ingredient in making myelin is fat. If they are put on a calorie restricted diet from too young of an age it can cause serious developmental problems.