Which program administers federal funds that assist low-income families with child care?

The Child Care Bureau (CCB) is the correct choice because it specifically focuses on administering federal funds designed to assist low-income families with child care. The CCB operates within the Administration for Children and Families (ACF) and plays a crucial role in providing financial assistance and improving the quality of child care services accessible to families in need.

In contrast, the Office of Community Services primarily works on broader community and economic development initiatives and does not specifically target child care. The Office of Family Assistance is responsible for welfare programs and may include aspects of child care but is not exclusively dedicated to that area. The Office of Child Support Enforcement focuses on ensuring that non-custodial parents meet their child support obligations and does not deal directly with funding child care for low-income families. Thus, the Child Care Bureau's direct role in administering these funds makes it the clear and accurate answer.