I charged $12 a day for about the same amount of time but I was taking the child to school across town. I had the child from about 6:30 am until I dropped them off at school around 7:45 am. Most child care centers get about $11-$15 a day for after school care, which included a small meal/snack. I got the same amount for before school care and that included a full breakfast.
Four hours or more is considered to be full time care and deserves the full charge amount of a full day. If the child is eating breakfast and lunch in your home then you need more to cover the cost. You will need to prepare food they eat and not just whatever you want, they extra money is for food for them and you'll need to find out from the mom what she expects them to eat, what she considers a standard meal and go from there as to what to charge.
For example: If she thinks you should serve bacon, pancakes, fresh fruit, whole grain toast, and milk every day for breakfast instead of a wholesome cereal, milk, and half a banana then she is going to have to pay more for food especially because your time is worth money and hot water for washing dishes, soap for washing dishes, wear and tear on your stove and stuff, etc...all add up.