In order to play the audio from a Remote Computer on your local computer, your local Remote Desktop Connection client must be set up to forward the audio.
Windows.
Regardless of the Remote Computer being connected to: Click the "Show Options" button.
Click the "Local Resources" tab.
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Click the "Save As..." to save a file that save the audio setting for the connection to which ever computer you have specified in "Computer:" In the example image, This connection file will connect to as-ts-hipaa.ad.syr.edu.
Macintosh
Edit the current entry for the Remote Desktop Connection by clicking on the pencil in the upper right-hand corner
If the Remote Desktop Connection has not been configured yet click on the "+" button and choose "Add PC"
You can configure your computer's microphone to be forwarded to your Remote Desktop Connection when you are connected to it.
Press Save. Connect to the Remote Desktop Connection and test.