written by Allen Browne : "How do I update the Quantity On Hand each time an item is sold/used?"

The simple answer is: You don't! You calculate the value when you need it.

 The calculation is very simple: the total number acquired, less the number disposed of. Just use DSum() on the table of acquisitions to get the number acquired for any product. Another DSum() expression on the table of uses/invoices gets the number disposed of. For the simplest databases, that's all you need.