Wear in the inner joint of the half shaft shows up as a "clunk" or "pop" when applying power, or if severe, when lifting off the throttle. If you claim that you can hear it from the RHR side, replace the RH shaft.
What I would do is jack the rear of the vehicle, under the diff is fine but place axle stands on the rear jacking points as well. Then have an assistant get in vehicle and try to acclerate in first gear as normal. You will see the rear wheels rotating, at the same time you can listen for the noise and observe for anything that doesn't appear to be correct. (Please remember the dangers involved in doing this. Choke the front wheels and make sure your stands are 100% firmly supporting the vehicle)
Grab hold of the actual half shaft (RH), and try moving it in and out, up & down. You will see if there is excessive play in either the inner or outer joint.