If by "real" you mean a minting error, probably not. American coins ( and most others) are made in dies that press the obverse( heads) and reverse(tails) into the coin at the same time so it is hard to imagine how a penny could be mis-minted in such a way. There are double headed coins made and sold as "gag" items, "let's toss a coin, 'Heads I win.' " I have never even heard of a double tailed one. The coins are not usually made by slicing the coin down the middle like bread and then fastening them together. Instead one coin has the tail side ground out just inside the rim, so there is a hollow round hole, another coin has the tail side ground down untill it is the thickness of that hole's depth then the rim is ground off so that its dimeter is the same as the hole's. The thin coin is fastened in the hole. Usually these coins are larger than a penny, it is easier to work on a larger coin and most people when tossing a coin use at least a quarter. But evidently you have a double tailed penny made that way. Use a strong magnifier and look just inside the rim along each side and see if you can spot any misfit. Go ahead and check the outer edges too just in case it is made that way. So it's not worth a red cent, except as a curiosity. But I tell ya what, just to make sure let's flip for it, if I win I'll take the penny and sell it just to see what its worth. We'll use a real quarter that we both examine just to keep it fair. Ready? Heads I win, tails you lose.

its probably worth quite a bit being a misprint so hang on to it. ive seen them go for thousands

I would say yes but am not an expert a coin dealer or some more research on it would be required. but don't let it go until you know for sure.