on the afternoon还是in

on the afternoon和in the afternoon都正确。通常说“在下午”但不具体指出日期,应该用in the afternoon.例如,I went to the cinema in the afternoon.如果是说某具体日期的下午就要用on the afternoon.例如,North Korean forces occupied Seoul on the afternoon of June 28.这和说“在某日”要用on是一致的。

in the afternoon和on the afternoon的区别为：指代不同、语法不同、侧重点不同。

指代不同

in the afternoon：在下午。

on the afternoon：下午。

语法不同

in the afternoon：一般说“在下午”用介词in,但当afternoon前有修饰成分如“某日的下午”或“星期×的下午”时用on,但当其前又有时间状语时, on也可换为in。

on the afternoon：afternoon与this, that, yesterday, tomorrow, every, all等限定词连用时相当于副词短语,其前不使用介词。afternoon用作状语时，其前也不使用介词。

侧重点不同

in the afternoon泛指“下午”，如：They have sold up ten crates of mineral water in the afternoon。他们一下午就卖完了十箱矿泉水。

on the afternoon：on the afternoon一般指具体某一天的下午，如：on the afternoon of June 5th。6月5日下午。