I know the incident table have a field called reopen_count that tells you how many times a resolved incident was send back to in progress. But I don't see a field like that for the sc_task table.
Once a sc_task record (catalog task) is closed complete (or incomplete or skipped) then active is turned to false and many data policies kick in so a normal user cannot reopen a catalog task. This is why the question is strange and something only an admin could do.
So another way to rephrase your question is: how many time the sc_task turned from active=false to true.
You could create a METRIC for that table that tracks the ACTIVE field. Then you generate a report that shows you how many have more than 1 metric.
I think a metric as Sebastian suggested is probably a better way to do this, but I would also like to add an alternative. When you close a task, it populated the "Closed" field. When the state is set back to "Pending" / "Open" / "Work in Progress", you may be able to utilize this functionality to display tasks which were previously closed, like so:
