FF is the least often used relationship and good examples are hard to come by. (I have to admit that I have never come across this relationship myself either.)
In this relationship, the succeeding activity cannot FINISH until the preceding activity has ultimately been concluded.
This really means that your example doesn't really fly either, because the building inspection cannot START until the plumbing, electrical and painting are finished. So it really is a Finish to Start relationship. (You could argue that you cannot FINISH it, if you cannot START it - but you try and get a building inspector to start inspecting the house before you've completed the plumbing and you'll quickly learn from him that it's a finish to start relationship. Maybe not with these exact words but he'll be quite clear.)
One example I heard of is writing a book: You have a task "write complete book" and "write final chapter". The moment you write the last word in the final chapter you have completed both tasks. Both end at the same time. The end of one is the end of the other. (It's not a great example, but it works better.)
If you look into the literature you'll see that the PMBOK definitions of these 4 relationships have changed over the years and that we struggle to give a good & clear example to explain FF.
What to do for the PMP Exam?
Don't worry about it. You won't be asked to give an example. You may be asked to review a network diagram and identify FF or you may be given an FF relationship and need to calculate total duration of a branch.
So as long as you can recognize it and apply it you won't have any trouble on the exam.
During my discussion with colleagues, my thinking if Finish to Finish relation example that I gave was as following:
There are multiple activities going on in parallel like plumbing, electrical, paiting for a building. The building is supposed to be handed over to the customer on 31-Jan-2011. All the activities will have the end date of 30-Jan-2011 as date for completion. On 31-Jan the inspection will be done and handed over to the customer.