the 200 mile-journey or the 200-mile journey
Solution 1:
200-mile is correct. It is a compound adjective derived from an adjective+noun phrase as in: The journey was 200 (adjective) miles (noun). Note the noun is made singular in the conversion. It is common with numbers + noun, as in a three-metre rope, a 60-kilogram rock. Addition of a postpositive adjective to these can cause confusion. As in the pool was three metres deep = a three-metre-deep pool, NOT: a three-metre deep or three metre-deep or three metre deep pool.