In this extract, the word famished at the end is reminding us of how hungry she is since she had not eaten since 3:00 pm, that is why her stomach is growling. The correct option would be "starving", it is a synonym of famished because it means to suffer or die of hunger. From the four given options, only the word starving implies something negative.
The word satisfied, which means having had enough of something in a good way, would be incorrect in the sentence since there is no textual evidence to support this meaning. Remember we said that her stomach was reminding her, and that happens when the stomach is empty.
The other two options, content and happy, are synonyms themselves. Both of them imply the idea of peaceful happiness and satisfaction. In consequence, neither of them has any similar meaning to the word famished.