Durante o desfile de moda, cada marca mostrou chapéus elegantes.

durante is a preposition meaning “throughout” or “during” when followed by a noun or noun phrase. It marks a time span.
By contrast, enquanto is a conjunction meaning “while” and must introduce a clause with its own verb.
Examples:

• Durante o verão, choveu pouco.
• Enquanto chovia, ficámos em casa.

You cannot say durante chovia because durante needs a noun, not a verb.

The preposition de links two nouns in a “genitive” or “of” relationship.

• desfile = show
• moda = fashion
  So desfile de moda literally means “show of fashion,” i.e. “fashion show.”
  If you drop de, you break that link: desfile moda is ungrammatical.

• cada means “each” or “every.”
• It is always singular and agrees in gender with the noun it modifies (but never changes for number).
  • Feminine: cada marca, cada casa
  • Masculine: cada homem, cada dia

You cannot say cada marcas – it must remain singular.

The subject of the verb is cada marca, which is grammatically singular.
Portuguese verb agreement follows the subject, not the object.

• Subject: cada marca (singular)
• Verb: mostrou (3rd person singular)
• Object: chapéus (plural)

If the subject were plural (e.g. as marcas), you would say mostraram.

In Portuguese, descriptive adjectives most commonly follow the noun:

• chapéus elegantes (elegant hats)
  Agreement rules:
• Number: chapéu → chapéus, elegante → elegantes
• Gender: hats (masculine plural) → elegantes (masculine plural form is identical to feminine plural for this adjective)

The order (noun + adjective) is standard for neutral/descriptive emphasis.

Yes, mostrar is a transitive verb that can take a direct object without a preposition:

• Eu mostro o livro.
• Ela mostra os chapéus.

If you specify to whom you show something, you add a (indirect object):

• Ela mostra os chapéus ao público.

You can say elegantes chapéus, but it’s less neutral and often more poetic or emphatic.

• chapéus elegantes = straightforward description
• elegantes chapéus = highlights the elegance, stylistic choice
  In everyday speech and writing, noun-first order is preferred for simple descriptions.