Please note that, in general, F-2 and H-4 visa holders are not eligible for work authorization. In cases where the F-2 or H-4 dependent was included in a Form I-485 (Petition for Adjustment to Permanent Residency), s/he may apply for an Employment Authorization Document (EAD card). The dependent should consult with the primary visa holder's attorney for further information on the possibility of filing for an EAD card.
Please note that working with an Employment Authorization Document may mean that the dependent loses F-2 / H-4 status but is still legally present in the U.S. as a Pending Permanent Resident. The F-2 / H-4 visa holder should speak with a qualified U.S. Immigration Attorney before commencing any employment.