Answer: Artificial Selection is the the process of taking 2 organisms (plants/animals) with desirable traits, or traits they want in future generations, and breeding them together.
Natural Selection is NOT correct because it does not apply to the question. Respectfully, you can look at Natural Selection as "Survival of the Fittest" (Explained by Charles Darwin), the organisms that adapt and overcome harsh conditions in their environment live on to produce more offspring that are ALSO adapted to the environment.
Variation also is NOT correct because Artificial Selection actually decreases the chances of variation in the future.
Mutation is when a new DNA sequence is created for a certain/specific gene, making a new allele. However, mutation is mainly caused by environmental factors, such as Ultraviolet radiation from the Sun.
In conclusion, the process described in the question is called "Artificial Selection."