The rise to the the idea of punctuated equilibrium is because of the incomplete transitional fossils; ie there aren't really any fossils that show a "transitional" state. (Even the archaeopteryx was shown not to be a transitional fossil just recently).
Now the question "How does the fossil record provide evidence?",
it provides evidences through contradiction, so due to the lack of fossils that show transitioning between to species (what we would expect in Darwinian theory) we can conclude that punctuated equilibrium is more likely.
Have a look at this:
http://evolution.berkeley.edu/evosite/evo101/VIIA1bPunctuated.shtml
"No preservation: No fossils representing transitional forms are preserved because of their relatively small population size, the rapid pace of change, and their isolated location"
This is saying that no transitional fossils would have been preserved so therefore "
The fossil record shows that there are short periods of rapid change in fossil forms" is incorrect as there is no transitional fossils to show rapid change. The fossil record only proves that there are long periods of "stasis" (no transitioning).
If the multiple choice had said ""T
he fossil record shows that there are long periods of stasis in fossil forms" then this would be correct.
Therefore this leaves A to be most correct, it shows evidence for punctuated equilibrium by having the fossil record incomplete. (incomplete meaning there is a lack of transitional fossils)
The whole idea of punctuated equilibrium was an attempted excuse to explain the lack of transitional fossils, not because there was several fossils found within a short time that showed rapid change from one species to another (and as explained above if this did occur we wouldn't have been able to discover them).
If i need to explain further just ask