Short version
The NSW BDM Registrar General Office was not set up until mid 1850's.
They did not receive the marriage records from the years prior to that until the mid 1880s.
Even now, they still have not completed the reconciliation processes to complete their records for marriages pre WWI.
JM Comments
So, a clerk in Sydney NSW BDM decades after an Elizabeth A Peisley had married a chap at Carcoar in 1854 needed to include that marriage on the HO registry. The clerk is reading a handwritten record. The clerk does not recognise the handwriting, and reads the surname as Hyde.
JM Question Is it likely that the surname was Flide ...
JM Answer Yes, it could well be Flide, perhaps the Carcoar C of E parish records will have the entry.
Cheers, JM