"A boy and a girl."
Translation:Bachgen a merch.
I had to consult a book for this (The Welsh Language: A History by Janet Davies(really recommend it) where there is a map showing where each word for girl is used. It seems as though hogan is used throughout the north with some usage creeping into the more southerly areas around Aberystwyth.(The book doesn't have a map for hogyn but I assume it is pretty similar.
I believe you are wrong.
King writes in his grammar that
In the literary language, a is followed by [Aspirate Mutation]: bara a chaws bread and cheese, halen a phupur salt and pepper, mam a thad mother and father. This usage is generally disregarded in the spoken language (see §9).
So a merch would be correct -- either aspirate mutation (which doesn't usually affect /m/) or no mutation. (Or, perhaps, a mherch; I have read that colloquially, m sometimes turns to mh under aspirate mutation; King calls this "common spoken practice of long standing which, however, is not presently accepted as part of the standard written language".)
Merch and Hogan are two of the more recoginsed words for girl so there would be no loss in understanding. That said I personally would usually pair up hogyn and hogan, and bachgen a merch. If in doubt in spoken Welsh you can always just say hogs for a group of boy and girls.(at least in the north where I live)