If the child is under 19, or under 24 but a full-time student, there is no specific dollar amount. The child simple needs to earn less than half their own support (costs for food, housing, transportation, clothing, medical, etc.)
If the child is over the age limit but is permanent and total disabled, the rule is the same, they must earn less than half their own support. But disabled for IRS purposes means "unable to perform gainful work" and $8800 earned from a job is indication that the child can perform gainful work. (Money earned at a sheltered workshop does not count as money earned from gainful work as long as the main reason the child is at the sheltered workshop is to receive medical care.)
If the child is over the age limit, and not disabled as defined by tax law, then you can't claim the child as a dependent if they earn more than $4050.
