I was taking apart a mtd yard machine 21 inch push mower, and noticed that the plastic tube connecting the carburetor to the engine had broken, and I need some help finding it's part number
Sounds like the intake manifold. But we'll need more info to get the part number for you.
If it's a briggs and stratton engine, the model number will be stamped into the metal engine cover above the spark plug, or muffler.