Translation:I would like to use the fitting room, please.
As an American native speaker, I would use "dressing room" or "fitting room" in a shop. "Dressing room" would be used backstage by actors getting into costumes. "Changing room" would be appropriate in a gym or swimming pool where a person is changing from street clothes to special activity clothing.
I am also a native (American) English speaker. I use "dressing room" for the box with a mirror in stores. And our stores also have that on directional signs telling us where to find them. I know that "fitting room" describes the same thing, but nobody uses this term. SO! It sounds like a regional difference - very fun! I have lived in Southern California most of my life, for reference.
June 12 2020 I also found that the female bot voice made it harder to hear all the words in the sentence. However, that is always my complaint with this female bot voice. It's just something one has to live with on Duolingo though I do appreciate that it is free and helping me to learn Spanish. Sometimes though she makes me want to scream in frustration!
There is a SpanishDict article on this: https://www.spanishdict.com/answers/217232/quisiera-or-me-gustara-