The correct answer is: Nobody knows everything he or she can about the brain.
Explanation:
There are different types of pronouns. They help to replace the noun in a sentence. In this case, the word "<em>Nobody</em>" is part of the indefinite pronouns and they are always used in the singular. So, it is necessary to change the personal pronoun "<em>They</em>" for the singular "<em>He or She</em>".