Broken cabinet door.. Need help in identifying the part
I don't think you'll find those anymore, they're pretty old. But, they're called Cabinet Brackets/Braces, Plastic Brackets/Braces, Screw Blocks, Angle Brackets/Braces, Modesty Blocks.

I'd suggest the left Metal L-bracket below &amp; screw in a new location, just to the left or right. Unless, the old holes still hold strong &amp; can actually tighten down very well with no slipping or spinning.