according to the manual for that motherboard, it supports crossfire.
the RX 580 supports crossfire as well.
So in short, yes, but, both cards will run at the slowest cards speeds for GPU and VRAM, and you will only have access to 4 of the 8GB on the 8GB card.
If you can get another 4GB version for cheaper then do that and don't waste the money on the 8GB version.
If you already have purchased/gotten into your possession both of these cards then my last point is moot.
But of course I would say that you should double make sure you have a power supply that is up to the task of powering both cards at the same time.
while it is true that the days of running more than one card in tandem are pretty much over, it is entirely up to you if you still want to do it or not.
if you already have both cards, and try running crossfire and don't get results you are satisfied with, and then decide to switch back to a single card, then yes, the 8GB card is the one you should keep.
If you have yet to purchase the 8GB card, then it is highly recommended you don't waste such money, since crossfire would probably not result in anything that is worth the investment, and going from 4GB to 8GB on the same GPU would not do much of anything to boost performance in games.
If you already own the 8GB card and were looking to get your hands on the 4GB for crossfire, don't.
it becomes the same argument made for buying the 8GB. waste of money.
perhaps taking the money you were going to spend on the second GPU (assuming you were going to buy it) and putting it towards a more powerful GPU instead as an upgrade then selling off your current GPU to recoup some of the cost for the upgrade would be a better idea.
Thank you very guys for the reply and answering my question.
I did not buy yet the RX 580 8gb gpu card, will be best if il buy 4gb rx 580 since i have a 750 true rating 80 gold? what is the total power for consumption?
or ill sell the old one RX 580 4gb then get a new one 8gb?