The sentence you wrote is almost correct but can be made clearer for a 4-year-old. Here's a better version:
The brain has two halves: the left side and the right side. Each half controls the opposite side of your body.
Explanation of changes:
- Changed "works" to "controls" because it better explains what each side of the brain does.
- Kept "opposite side of your body" because it's true and easy to understand.
- Made sure the sentence is simple and clear for a young child.