This part is especially hard because there's very specific overlap.

If a noun is the direct object it will be in the accusative case.
This means it is the primary conceptual receiver of the verb, as opposed to a secondary receiver, or an object of a preposition.

Any adjectives affecting a noun, must match in gender-case-number.

Now, it's important to note, that what exactly the accusative case looks like can vary.

When talking about these sorts of things, the Nominative Singular is considered to be the default state of a noun.
For Adjectives, the Nominative Singular Masculine is the default- dictionary form. Mostly: -ый, -ий

The Accusative Singular and Plural of a Masculine Noun has one of two options:
If the Noun is "animate", it will be formed with the same ending as the Genitive Singular.
If the Noun is "inanimate", the Accusative looks just like the Nominative.

There is a complex logical circuit explaining why this is okay, sensible, and works, but it's a lot to explain

Feminine nouns are usually easier:
For Feminine Nouns ending in -а, the Accusative ending is -у.
Nom - Acc
а - у
я - ю

Подруга
https://en.wiktionary.org/wiki/%D0%B...83%D0%B3%D0%B0
(Don't look at the PreReform declension, that's not important, mostly obsolete spelling)

https://en.wiktionary.org/wiki/%D0%BC%D0%BE%D0%B9

Мою подругу из России зовут "Катя".
If you ask me, the quotes around Katya are grammatically important.