Joe-ah-KEE-no roh-SEE-nee
Here's a breakdown:
* Gioacchino:
* Gio: Pronounced like "Joe"
* acchino: Pronounced like "ah-KEE-no"
* Rossini:
* Ros: Pronounced like "roh"
* sini: Pronounced like "SEE-nee"
The emphasis is on the second syllable of each part of the name.