There could be many different causes for this, but assuming the iPod Touch works perfectly fine (and never had an incident where it shorted out, had to be repaired, dropped in water, etc.), the first step is to make sure that the headphones are plugged in all the way. Shorting out of the sound in the right headphones is common when the headphones are not blugged in all of the way. The second step is to try out a friend's headphones are just get new ones, because if you try out a friend's and it works fine, then you know it is your headphones and you need to get a new one. The headphones don't cost that much, so it's better just to buy new ones if you already followed the first step.