"Chci jiný klobouk."

Translation: I want another hat.

[Chessnecof]

I thought dalsi would be another, jiny a different

[BoneheadBass]

Both can be translated as "other" or "another." But, yes, další has the sense of "additional," while jiný has the sense of "different."

[AdrijanaJa1]

I translated as "I want different hat". Considering what you say, why is it wong?

[BoneheadBass]

"I want a different hat" is accepted. You need the article "a" here, and your reported answer does not include it. (Thank you for reporting, though!)

[AdrijanaJa1]

Thank you for fast answer and a lesson! That article "a" is killing me... I keep forgetting on it as I'm not native English speaker... :)

[Jaro488307]

why no i want the another hat.. by me it us not possible only hat.. without.. a hat..

[AgnusOinas]

"another" = "an" + "other"

You should probably spend more time in courses that teach English. This course is primarily for those that want to learn Czech.