Nagasaki
proper noun
This word will be easier if you jump to the reading, since it's the name of a place, Nagasaki.
The 長 is the kun'yomi reading, which comes from 長い. The 崎 part is the same reading that you learned with the kanji (though also kun'yomi). Combine those together and you have ながさき. Sound familiar? It should. This is the city of Nagasaki, one of the cities in which the A-bombs fell.
あなたへのお土産に長崎カステラを買いましたよ。
I bought some Nagasaki sponge cake for you as a souvenir.