Controlled mating between closely related animals of the same breed for 4-6 generations is known as ______________ .

The correct option is B inbreeding
Animal breeding is an important part of animal husbandry, that includes controlled mating of domesticated animals followed by the selection of offspring with superior genotypes. Animal husbandry refers to the caring and breeding animals for various products like milk, meat.
There are two types of animal breeding namely, inbreeding and out- breeding. Out-crossing, cross-breeding and interspecific hybridisation are the types of out-breeding.

Inbreeding is a type of animal breeding which involves mating closely related animals within the same breed for 4-6 generations.

Out-crossing refers to mating animals of the same breed, provided they have no common ancestors on either side of their lineage for the past 4-6 generations.

Cross-breeding is a type of animal breeding that involves mating two animals belonging to two different breeds of the same species. For example, Hisardale a breed of sheep has been developed by crossing Bikaneri ewes and Marino rams.
So, the correct answer is inbreeding.