後で and 三時間後: later versus a measured interval
Compare a later phone call with an arrival three hours after departure, identifying the starting point of the interval.
Later without a measured delay
後で, read あとで, means later. 後で電話します。 says that the person will call later without specifying how many minutes will pass.
会議の後で話しましょう。 suggests talking after the meeting. The meeting supplies a reference event but no precise delay after its end.
After a specified length of time
三時間後, read さんじかんご, means three hours after a reference point. 出発の三時間後に到着しました。 says that arrival occurred three hours after departure.
今から三時間後に始まります。 says that the activity starts three hours from now. 今から specifies where the interval begins.
Readings and reference points
後 is read あと in 後で and ご in 三時間後. The same written character can have a different reading in a different expression.
午後三時に始まります。 specifies three p.m. 三時間後に始まります。 instead locates the start three hours after a reference point. Keep the clock time 三時 distinct from the duration 三時間.
Is now the interval’s starting point in 出発の三時間後に到着しました。?
Show the answer and why
No. 出発の identifies departure as the starting point. The sentence reports a past arrival three hours after that departure.