山間 and 郊外: mountain terrain and a city's outskirts
Compare mountain villages and travel with a park in the suburbs, keeping terrain separate from a place's relation to a city.
Mountain terrain in 山間
山間（さんかん） means a mountain area or a place among mountains. 「山間の小さな村に古い祭りが残っている。」 says that an old festival survives in a small mountain village. 山間の describes the village's terrain-based location.
「列車は山間を縫うようにゆっくり進んだ。」 describes the train moving slowly along a winding course through the mountains. The route and ゆっくり describe its movement; distance from a city is not supplied.
郊外 in relation to a city
郊外（こうがい） means suburbs or outskirts. 「週末に郊外の大きな公園を訪れた。」 describes visiting a large park in the suburbs over the weekend. 郊外の places the park in relation to the city.
The sentence does not state whether the park is flat or among mountains. 郊外 alone does not establish terrain or a numerical distance from the city.
Two separate criteria
山間 uses terrain among mountains as its reference. 郊外 uses the relationship to a city. One place can satisfy both criteria, so the words do not identify necessarily opposite kinds of areas.
The surviving festival, the train's movement, and the park visit supply different information. Combining the examples does not establish that the particular suburban park is in a mountain area.
Does 郊外の公園 establish that the park is flat or has terrain opposite to 山間?
Show the answer and why
No. 郊外 identifies the park's relation to a city's outskirts; terrain requires separate information. 山間 uses being among mountains as a different criterion.