Can’t hear USB keyboard in Logic Pro X

If you can record notes using your P6, it's not the keyboard to blame. Either the track you're recording on is muted, or some other track or region is solo-ed in the project. It might help if you make and post a screenshot of Logic's window.

Could you tell what kind of keyboard is it? Also, how is your audio output set up?

To set up Logic's audio output, go to Preferences > Audio > Devices tab. Select your audio interface (if you're using one) or Built-in Output (if you want to use your Mac's speakers) as Output device.