Can a parent with brown hair and a parent with ginger hair have a ginger hair child?

Yes, a parent with brown hair and a parent with ginger hair can have a ginger-haired child. Hair color is determined by multiple genes, and the ginger hair color is often recessive. If the brown-haired parent carries a recessive gene for ginger hair, there's a possibility that their child could inherit that gene from both parents and have ginger hair.