"Де мої коричневі шорти?"
Translation:Where are my brown shorts?
Brown is an adjective (кори́чневий), here it's in its plural nominative form. Шо́рти is also a nominative plural.
Шо́рти is a pluralia tantum noun, it only has the plural form. Other nouns like this are штани́ 'trousers', окуля́ри 'glasses', дрова́ 'firewood', вершки́ 'cream (eatable)', гро́ші 'money', ша́хи 'chess'. These nouns just don't have a singular form. (Although it may look that some of them do, e.g. there're words гріш 'small coin; grosz, Polish coin', and шах 'check (to the king), shah', they mean very different things and therefore are considered different words.)
The suffix -ев- ~ -ов- is characteristic for adjectives in Slavic, not nouns /except for the gen. case of the archaic u-stem nouns/. It denotes that something is "derived" or "produced" from the notion expressed by the root of the adjective. In this particular case, коричневий is formed by корица (which means 'bark, rind') + -нев- + inflection ending, i.e. denotes the colour "derived" from tree bark = 'brown'. You can also find this ending in Slavic names, e.g. 'Иванов' = "derived from Иван" ~ "begot by Иван".