"I want a different bag."
It marked me wrong when I wrote this using the kanji. I've reported it (Jan. 10, 2018).
違う is a verb so it connects to a noun with nothing but in its plain ending forms.
な is a connecting form of だ. It goes with the な-adjectives. Test if it should be な if you can and must end a phrase with だ/です。
きれいだ / きれいです OK >>>きれい な カバン
高いだ XXX / 高いです Optional >>> 高い カバン
持っているだ XXX /持っているです XXX >>> 持っている カバン
違う（ちがう） is not the main verb in the sentence, but rather as a descriptor of the bag: "a differing bag"/"a bag that differs [from another one]" - that is, a different bag.
欲しい（ほしい） is an adjective literally meaning something like "wanted/desired".
If you literally translate わたしはちがうカバンがほしいです, it means something like "As for me, the bag is wanted/desired." The は marks the topic (usually the person who wants something), and が marks the thing they want.
frustrating to have the tips in kanji and not use kanji in the exercise - i know I'm repeating a common complaint about this course but there needs to be some consistency with using kanji and finding a way to show furigana (even if its in parentheses after the kanji)
With "hoshii", you usually use は to show who wants the thing, and が to show the thing that is wanted.
Watashi wa chigau kaban ga hoshii desu.
I want a different bag.