Is it easy for breeders to produce mutants?

It depends! If we're talking about something like a cute little Matlipoo, your answer is yes. These are technically considered mutants as they posses characteristics that are not found in either of the original populations (Maltese + Poodles). Not all mutations are bad. Those who survived the bubonic plague are said to have a mutated gene that enabled them to be more resilient against the illness.

In the case of inbreeding the mutation can prevent offspring from being born by either causing sterility in the parents, or it will cause a miscarriage so the fetus is terminated naturally in the beginning. Sometimes the offspring is still born (deceased at birth), or has debilitating symptoms like in cerebral palsy. So there is a chance that the offspring may never be born, making it impossible for a breeder.

Mutations can also be spontaneous, so a breeder might mean well by selecting two animals from different family trees, but both of the parents could produce mutant offspring together.

This question is pretty vague, you should ask your teacher for clarification.