“Cro Magnons had killed out the Neanderthal prior to the arrival of Adam and Eve.”
Recent studies of the Neanderthal and Human genomes show a great deal of mating and reproducing in antiquity. Members of the same species are defined as being able to reproduce with healthy offspring able to reproduce as well. Thus, Neanderthals are simply human beings.
The photo you provided is not an accurate picture of a Neanderthal as well. Put a Neanderthal in a suit, clean him up, and you wouldn’t think he was a monkey-man.
Every bit of that is wrong. Neanderthal DNA was halfway between ours and that of a chimpanzee, and there is zero real physical evidence of humans and hominids ever cross-breeding. Genes which we share with hominids could more easily be explained as an original designer simply using a few of the same low-level genetic parts on dissimilar projects. Similarly, bank software and rocket telemetry software could easily use a few of the same low-level C language math functions; that would not indicate that NASA’s software was hacked from that of JP Morgan.