How old should a child be before he can take motrin or advil (ibuprofen)?

6 months. The usual recommendation is 6 months for Ibuprofen (motrin or advil). Some doctors may allow you to use it sooner. But the recommended age per their website/product info is 6 months.
6 mo. These come from a class of drugs that travel trough the kidneys to be eliminated from the body. The first few months the kidney is not quite ready to do the job and there is a potential for injury to these developing structures until the kidney is ready. It wouldn't effect them all but you wouldn't want your kid to be the one it did. The recommendations are based on science not preference.
Ibuprofen limit. Under a physicians guidance it can be taken at a younger age if absolutely necessary.