From this short distance, it is possible to pick out many man-made objects such as motorways, railways, cities, fields, and the Great Wall. However, you only have to travel ANOTHER few thousand miles (away) before all man-made objects FADE from view. (away is optional you can remove this word) From this short distance, it is possible to pick out many man-made objects such as motorways, railways, cities, fields, and the Great Wall. However, you only have to travel 57 kilometres THE OTHER way, before all man-made objects FADE from view. you can choose either. the other way implies means in a different direction. another 57 miles implies or would actually mean to continue in the same direction​.

Another is the right one. The other = something else Another = extra

Технически они налажали с этим выбором поскольку множеcтвенное после another может быть или после of или после количества (three, five) и они втулили сюда few thousand, а фактически нет грамматической базы подвести под "почему the other неправильно" которое подходит и по смыслу и по грамматике.