In hindsight, I have to admit it does look a little suspect with the homo sapiens brain reference in there. I only wanted to signify that we’re talking about a big species (like a buffalo, bear or deer).
Than you should have said that in the first place and I would not compare a deer with either a bear or a bison assuming you didn't really mean buffalo.
Find a site like this one and get anatomical targets to find out where hunters have learned to shoot game.
Your choice of guns made little sense either which is why it looks like you are trolling. Not many of us have 10 gauges because 12 has taken over what the 10 could do with 3 and 3 1/2" magnums 20 you wouldn't use on anything larger than a deer, your other choices are not hunting guns but if you aren't hunting but slaughtering a penned animal then a 38 special will do as good a job as the 10 gauge.
Mostly it would help if you would have stated why you wanted to know instead of the limited parameter you gave with no reason for it. If you answer is in the title, a downed wounded animal then any gun you downed it with to the skull will do it. Before you hunt learn your basic anatomy so you aren't just blowing holes in it's sinus cavities.