Learn Spanish (Latin America): ¿Puedo ver algún estilo diferente?

Algún is the shortened form of alguno. In Spanish, you must drop the -o and add an accent mark whenever it comes directly before a singular, masculine noun like estilo.

The English translation says "styles" (plural), but the Spanish sentence uses singular words (algún estilo diferente). Why?

When asking if you have or can see any of a certain thing, Spanish speakers almost always use the singular form (algún + singular noun). While English naturally defaults to the plural "any styles", saying algunos estilos would sound a bit unnatural here.

Why doesn't the adjective diferente change to match the masculine noun estilo?

Adjectives that end in -e (like diferente, grande, or inteligente) are gender-neutral. They use the exact same form for both masculine and feminine nouns. They only change if you need to make them plural by adding an -s.

Why is the verb ver left in its dictionary form instead of being conjugated?

When you use two verbs together to express a single idea, only the first one is conjugated. Since puedo (I can) is already conjugated to match "I", the second verb ver (to see) must stay in its infinitive form.