I copied and modified your picture and put a red circle around the numbers. You'll have to clean it off good to read them. The last 3 numbers of the larger set are what your interested in. Like Johnny said look for a 489, 741. or 742.
Pressure washing the entire rearend is a good idea cause right now it's such a mess it's hard to say exactly where the fluid is leaking from. Clean it up good and run it for a day then look at it again and you should be able to tell real easy what all is leaking. If it's just coming out of the yoke and it's a 741 or 742 carrier it's a real easy repair (well easy except for getting the nut loose and re-tightened cause it's torqued to 240 ft. lbs). Just remove the driveshaft and the yoke retaining nut and slide the yoke off. Clean things up, pop out the old seal and drive in a new one. Inspect the yoke good too cause sometimes it can get a groove worn where the seal rides. If that's the case there's 2 solutions. You can either replace the yoke or install a speedy sleeve that you can purchase at NAPA or any other decent auto parts supplier. I'm not crazy about speedy sleeves cause their not the easiest to get on without damaging them because their so thin. For that reason I usually just find a good used yoke. A good used yoke usually doesn't cost much more than a speedy sleeve. Yokes are interchangeable from all 3 8-3/4 rears. Just gotta get the right size and almost all A-bodies used the smaller 7260 yoke.