郊外 and 都心: where one lives and travels
Distinguish outskirts from the city center and follow residence, commuting, and moving.
A location on the outskirts
郊外, read こうがい, means the outskirts or suburbs. 郊外に住んでいます。 means living in the suburbs.
郊外の公園へ行きました。 means going to a park on the outskirts. It does not also establish that the person lives there.
The city center
都心, read としん, means the city center. 都心で働いています。 means working in the city center.
都心まで電車で三十分です。 says that the city center is thirty minutes away by train. 三十分 is travel duration, not a departure time.
Residence and commuting
郊外から都心へ通っています。 describes traveling regularly from the suburbs to the city center. から and へ identify the origin and destination.
都心から郊外へ引っ越しました。 means moving from the city center to the suburbs. Its direction is the reverse of the commuting example, so read the order carefully.
Where is the new residence in 都心から郊外へ引っ越しました?
Show the answer and why
In the suburbs. The move was from the city center toward the outskirts.