Тридцять одна машина is 31st car. And 31 cars is тридцять один машин.
машина is feminine, no way it can take "один". These Tips & Notes should help you: https://www.duolingo.com/skill/uk/numbers1
what's the problem with ''авто' ?
(instead of 'машина')
doesn't авто mean ''auto / car'' ?
Yes, it does. 'авто' is a short form of 'автомобіль'. Besides, there is 'автівка', a popular colloquial word for 'car' that is common in everyday speech and modern Ukrainian literature. All those variants should be accepted.