A compound adjective is an adjective that contains two or more words. If it is before the noun it talks about then it is joined by a hyphen. If it is after the noun it talks about then there is no hyphen.
- He is a world-famous artist.
- The artist is world famous..
- I would like to live in an English-speaking country.
- I would like to live in a country that is English speaking.
Common mistakes with adjectives.