Learn French: Cette matière est vraiment difficile. - This subject is really difficult.

In French, matière is specifically used for a school or academic subject. A sujet is a subject of conversation, a broad theme, or the grammatical subject of a sentence.

Why is the word for "this" spelled cette here?

Matière is a feminine noun, so it requires the feminine word for "this" or "that", which is cette. If the noun were masculine, you would use ce, or cet if it started with a vowel.

Could I use très here instead of vraiment?

Yes, but the nuance is slightly different. Très difficile means "very difficult," while vraiment difficile emphasizes that it is "really" or "truly" difficult. The word vraiment is an adverb built directly from the adjective vrai (true).

Why doesn't difficile have an extra "e" at the end to match the feminine noun?

Adjectives that already end in a silent -e in their default masculine form, like difficile, stay exactly the same in the feminine form. You do not need to add another -e.