In the context of the passage, the word "livid" means very angry. This is because Mary had been asking her neighbor to repair the fence on his goat pen to prevent the animals from getting out. When she saw the goat had scratched the hood of her car and was calmly eating a windshield wiper, she was furious. This shows that she was extremely upset or angry at that moment.
Therefore, the word "livid" in this context indicates a strong feeling of anger or fury.
