Your thrust washer part number is not showing up as a valid number so though I'm sure it worked fine with what you had, I would be hesitant to re-use it especially on your Yamaha engine running a new Mercury prop. Checking the fit with everything in place may tell a different story. The 12- number would make it a mercury part number and not a Yamaha number. If your buying a complete brand new prop in the box it may or may not (some do some don't $$$) come with a standard hub kit to fit a mid horse power range gear housing. If you had the "original" Yamaha "thrust washer" you should be able to use the rest of the hub kit that may come with the prop. If the new prop don't come with a hub kit either find/buy the Yamaha thrust washer and you should be able to reuse the black max flo-torq 2 (if that's what your black max prop you have now really uses. 50/50 on that) Or you would need to order Mercury flo-torq 2 hub kit # 835274Q1 that fits "your" Yamaha engine model.
http://www.iboats.com/Yamaha-Flo-Tor...view_id.486318
All that said above, I saw you ordered the new Flo-Torq IV Merc part # 835257K10? Mercury Hub Kit? if so, you must only use an original Yamaha thrust washer. The rest of the Merc kit should work but it's best to be prepared and always have a Yamaha prop nut kit at the ready.
Nice call on wanting to use the new Flo-Torq IV kit to help eliminate the 4 stroke low speed prop rattle.
Before installing the new flo-Torq IV, you really need to watch this installation video Mercury marine did to help with many questions.
http://www.youtube.com/watch?v=H4nTiGOcIvs ......
http://www.google.com/url?sa=t&rct=j...pqW3UJavvtZX1g
Please note that the Bravo 3 uses an entirely different set of thrust washer sizes.
Hope this helps, good luck.