If Mrs Ellis has 2/3 of a pizza left, this is the same as saying she has 4/6 of a pizza, this is because we can multiply both the top and bottom of the fraction by 2, and the fraction remains equal.
4/6 of a pizza left divided by the 4 children to feed, means we can divide the fraction by 4 to get how much each child gets, we can divide the top of the fraction by 4 to get 1/6. This means each child gets 1/6 of a pizza.