The problem could be with your REAPER settings or with your hardware set up. Make sure the track is armed for recording. Make sure that the track has been assigned an input. ... Check your audio input mixer (external hardware desk, sound card mixer software, or both) to make sure that the incoming signal is not muted.
How do I monitor sound in REAPER?
Right-click the "Record Arm" button on the mixer track channel you plan on recording to, then select the "Monitor Track Media While Recording" option from the pop-up list. This option lets you hear the audio being recorded as it is being captured.