The practice of mating closely related animals with one another is referred to as

The practice of mating closely related animals with one another is called inbreeding. In inbreeding, the animals involved share recent common ancestors - for example, mating a father with a daughter, a brother with a sister, or a mother with a son. The purpose is typically to fix desirable traits and increase genetic uniformity within a line, though it carries the risk of inbreeding depression (reduced vigour, fertility, and disease resistance due to increased homozygosity of deleterious genes).

The other terms describe different breeding practices:

• Line breeding is a milder, more controlled form of inbreeding that involves mating animals that share a common ancestor but are not as closely related (e.g., cousins or grandparent-grandchild). While related to inbreeding, the question specifically says "closely related," which points to inbreeding proper.
• Cross breeding is the mating of animals from different breeds to combine desirable traits and often produce hybrid vigour (heterosis).
• Hybridization refers to crossing animals (or plants) of different species or significantly different genetic backgrounds, which is a broader concept than cross breeding within the same species.

Exam tip: Inbreeding = mating closely related animals (high genetic similarity). Cross breeding = mating animals of different breeds. Line breeding = a controlled, less intense form of inbreeding.