The type "在…上" (zài...shàng) can express the position exactly where an action takes spot or perhaps a condition exists. The type在…上can also be employed to indicate scope or aspect when an abstract noun or verb is utilized in between. For instance,
他在楼上。tā zài lóushàng. [He is upstairs.]
他在班上的表现还是不错的。tā zài bān shàng de biǎoxiàn háishì bú cuò de. [He performed well in the class.]

The type "在…下" (zài...xià ) can indicate a concrete place or it might indicate a condition or situation. For instance,
在妈妈的帮助下，我完成了功课。zài māmā de bāngzhù xià, wǒ wánchéng le gōngkè. [I finished the homework with my mum’s help.]
在他的陪伴下，我去香港玩了一周。zài tā de péibàn xià, wǒ qù xiānggǎng wán le yīzhōu. [I visited Hong Kong for one week with his company.]

Phrases with “的” (de)
Phrase is one where the structural particle "的" is attached to a notional word or phrase. For example,
这本书是我的。zhè běn shū shì wǒ de. [This is my book.] ("的" is attached to a pronoun)
这条裙子是红色的。zhè tiáo qúnzi shì hóngsè de. [This is a red skirt.] ("的" is after an adjective)
比赛的有八个人。bǐsài de yǒu bā gè rén. [There are night people attending the competition.] ("的" is after a noun.)