向こう and 対岸: beyond a reference and on the opposite shore
Compare a view beyond a window with the opposite riverbank, without restricting everything described by 向こう to a shoreline.
Beyond a specified reference
向こう, read むこう, points beyond a reference or over there. 窓の向こうに庭が見えます。 says that a garden can be seen beyond the window.
道の向こうにいる人は先生です。 identifies the person across the road as the teacher. 道 supplies the separating reference.
The shore across a body of water
対岸, read たいがん, is the opposite shore across a river or lake. 川の対岸に船着き場があります。 places a boat landing on the opposite riverbank.
対岸の人に手を振りました。 says that someone waved to a person on the opposite shore. It does not state movement toward that person.
A broader area beyond versus the shore itself
川の向こうに山が見えます。 says that a mountain can be seen beyond the river. It does not place the mountain directly on the bank.
対岸まで泳ぎました。 says that someone swam as far as the opposite shore. Preserve the endpoint specified by まで.
Must the mountain in 川の向こうに山が見えます。 stand directly on the riverbank?
Show the answer and why
No. It is visible beyond the river, and the distance between the bank and the mountain is not specified.