Suns Orbital speed and escape velocity question
It's asking exactly what it says- where would you expect this material to end up? Giving a distance from the center of the galaxy may be relevant, or it may not, depending on exactly what speed you end up with, and how it compares to galactic orbital / escape velocity. If the velocity is well above galactic escape velocity, giving a specific distance from the galactic core doesn't make much sense- there will be no fixed distance, the stuff will just keep going, achieving greater and greater distances.

So, the first step is indeed to solve and check if average speed > orbital velocity or not (because the question says to do so), and a good second step would indeed be to check if it's less or greater than escape velocity. And from that information, you can guess generally where the stuff will go- stay reasonably close to the original orbit of the star? or stay in galactic orbit, but spread out in some wildly different range of orbits than what the original star had? or completely ejected from the galaxy?