Do we capitalize adjectives

No, you don't generally capitalize adjectives. However, you would if you are using proper nouns (names, often in possessive form) as adjectives.

Examples:

I have a green crayon. - Ordinary adjective.

Someone stole John's car. - Proper noun possessive used as adjective

The meeting was at the Filmore Center. - Proper noun used as adjective in a prepositional phrase.

She visited the White House. - White House is a proper noun, and white modifies house.