Re: 第二/另外 (another) grammar question

「第」act like a prefix that mean  "next " or "some other"

Examples:
第次 ~  next time / some other time
第時 ~  next time / some other time
第個 ~  some other one
第日 ~  some other day


** 「第二」simply mean " the second / the next " 

Examples: 
「第二個」~ the next one
「第二日」~ the next day / the second day
「第二次」~ the second time
「第二名」~ the second place / the second one

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「另」act like a prefix ~  "separately " or "differently"

Examples:
「另選」~ choose differently / choose separately
「另付」~ pay separately
「另聘」~ hire another 
「另娶」~ marry another (wife)
「另嫁」~ marry another (husband)

**「另外」 simply mean  "separately"

Examples:
「另外選擇」~ choose separately
「另外付款」~ pay separately
「另外聘請」~ hire separately 

For " another" as in " choose another " the common way to say it in Cantonese is 「第二個」  or 「另一個」

「可唔可以揀過(另一個)？」~ 「can I pick (different / another ) one?」
「可唔可以揀過(第二個)？」~ 「can I pick (some other  / another ) one?」

Both 「另一個」 and 「第二個」 are equally common.