Ok, here is the solution they gave.
Is there an easier way to do it?
Cool! They've done it the best/easiest way, let me explain!
We know that a certain amount of work, 1MJ, is needed to move the object from 10,000km to 20,000km. This energy goes directly to a change in GPE. So, the 4 lines at the top are saying, "We know that the difference in GPE at the two heights is equal to work done. Let's use that." In this case, we use it to find the grouped value of the constants \(GMm\).
So now we have \(GMm\) - And we need to find the energy required to move from 20,000km to 80,000km. This is now just formula work - The last 3 lines involve calculating the difference in GPE at those two radii
(Note - They do factor out the \(GMm\), don't let that confuse you, it is still just GPE!
Does that help give it some context?