What is the difference between credit hours carried and hours earned?
If you want an authoritative answer, contact your university's registrar office.  Terms like this are not completely standard around the world, so we can only guess as to what they mean at your institution.

I would guess "carried" counts all the classes you have taken, but "earned" counts only those which you have passed.  So on the first line, the extra 8 hours might represent some classes that you failed, or that you are currently taking and have not yet completed.  "LSU" probably counts only those hours corresponding to classes taken at LSU, while "Cum" (presumably standing for "cumulative") might also count classes transferred from other institutions.