Bike headset loose, how do I tighten it?

I got my son a used mongoose bike off Craigslist, the bike works pretty well but the headset is loose as you can see in the video, I don't think that by tightening the nut it will fix it, but I also don't have a big enough wrench to try to tighten it. Anyone knowledgeable enough to tell me what I need to do to stop it from wobbly back and forth? Side to side it's solid, just forward and backwards it wobbles

Thanks

thank you for everyone's advice, I finally found a wrench big enough to take that nut off, I found that the nut underneath it was loose, once I tighten it then it wasnt wobbly anymore. I did take the whole fork off the frame and some ball bearings came outta the tube, not sure if that was suppose to happen. at first I thought it might be the bottom of the cup that lost its bearings, but when I tried to put in the bearings from the top of the cup to the bottom of the cup, it doesn't seem like it belong. I just put everything back together and it seems like it's working fine now even though there is a possibility that the bottom of the frame to where it matches the cup at the bottom might not have bearing?