Sure, I think that this means that the try the normal case and the flipped case.

> ie. compare both hash(enteredPassword) and hash(invertCase(enteredPassword)) to the hash in the database and see if either match

Here's an example in bash:

  $ echo PasSwoRd | tr 'A-Za-z' 'a-zA-Z'
  pASsWOrD

In the database store one variant

  $ echo PasSwoRd | tr 'A-Za-z' 'a-zA-Z' | sha256sum > db

Then you can test both on input

  $ echo PasSwoRd | sha256sum > sum1
  $ echo PasSwoRd | tr 'A-Za-z' 'a-zA-Z' | sha256sum > sum2
  $ diff -q db sum1
  Files db and sum1 differ # i.e. LOGIN FAILS
  $ diff -q db sum2
  $ # i.e. LOGIN SUCCEEDS

The problem with the caps lock behaviour on Macs is harder. You definitely don't want to force to uppercase!