A Power Series is very similar to a Taylor Series, but they're not exactly the same thing. A power series is of the form
Whereas a Taylor Series is of the form
So, you can see that a Taylor Series is a Power Series, but a Power Series is not necessarily a Taylor Series.
Okay, now, it's been a while since I've dealt with a Power Series expansion, but I believe what you're supposed to be doing here is taking your initial series, 1/(1-t), and modifying this series to get the new, listed series.
So, in order to do this, we need to list the steps necessary to change 1/(1-t) into the form 4/(x^2 -2x). List the steps required to change the one series to the other, and then perform these operations on the entire summation. This will be your new Power Series expansion.