No ducks and geese cannot mate. There are certain types of ducks that interbreed such as mallards and black ducks. And certain types of geese such as the different Canada geese sub-species. But no, ducks and geese cannot interbreed. read more
basically what you have between your duck and geese is the very common species barrier, rendering it impossible for the duck and geese to have offspring, but it is not impossible for them to mate. read more
ducks and geese, although able to breed, are unable to produce offspring due to different chromosome numbers (same species and interbreedable species have the same number of chromosomes, this produces viable, fertile offspring). read more