GA flight instructor reported pilot flying mistook taxi instructions resulting in a runway incursion.

Narrative

I was flying with a private pilot for our flight school this morning in Aircraft X; and we had an incident happen that I wanted to report; the incident occurred in ZZZ; we were on flight following to ZZZ1; we were holding short for Runway XXL ready to depart and reported holding short for the landing traffic insight; there was a traffic on short final for that Runway XXL; we got advised to hold short for landing; there was another traffic getting cleared; we were verifying the way points and flight plan before departing; the private pilot got confused with the tail numbers of the other aircraft heard the last two numbers and added power while reading the call to Tower thinking that we were cleared for the takeoff; I held the brakes as we crossed the hold short line; the front quarter of plane crossed the hold short line and Tower told us that the call was to a different airplane; the plane on short final decided to go around; we were advised to copy and call the number. I learned from this to keep a more longer safe distance from the hold short line; and always have my brakes on holding short of runway even flying with someone until verifying the right call from Tower clearing me for departure. This is a good lesson of verifying calls; before further advised of anything.