The main idea is that when you busy people’s minds with a routine task, they are less able to rationalize their own behavior and they are more likely to report the truth about what they are doing. The most quotable excerpt assumes a bit of context
To find out, he and Dr. Valdesolo brought more people into the lab
and watched them selfishly assign themselves the easy task. Then, at
the start of the subsequent questioning, some of these people were
asked to memorize a list of numbers and retain it in their heads as
they answered questions about the experiment and their actions.
little bit of extra mental exertion was enough to eliminate hypocrisy.
These people judged their own actions [in assigning themselves the easy task] just as harshly as others did.
Their brains were apparently too busy to rationalize their selfishness,
so they fell back on their intuitive feelings about fairness.
If you wish, here is the whole piece.