**Core Concept**
The family life cycle is a theoretical framework used to understand the stages a family goes through from formation to dissolution. It is a crucial concept in family dynamics, social sciences, and preventive medicine. The family life cycle model helps in understanding the needs and challenges faced by families at different stages.

**Why the Correct Answer is Right**
The complete extension phase is the stage of the family life cycle that begins with the birth of the last child and ends with the leaving of home of the first child. This stage is characterized by the expansion of the family, with the addition of new members and increased responsibilities for the parents. During this phase, the family's needs and dynamics change, and they must adapt to the new challenges and opportunities presented by the growing family. The complete extension phase is a critical period in a family's life cycle, as it sets the stage for the next phase, which is the contraction phase.

**Why Each Wrong Option is Incorrect**
**Option A:** Formation is the initial stage of the family life cycle, which begins with the union of two individuals and ends with the birth of the first child. It is not the stage that begins with the birth of the last child.
**Option B:** Extension is a broader term that refers to the expansion of the family, but it is not a specific stage of the family life cycle. Complete extension is a more accurate description of the stage beginning with the birth of the last child.
**Option D:** Contraction is the stage of the family life cycle that begins with the leaving of home of the first child and ends with the death of the last parent. It is not the stage that begins with the birth of the last child.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the family life cycle model is not a linear progression, and families may experience overlapping or reverse stages due to various factors such as divorce, remarriage, or blended families.

✓ Correct Answer: C. Complete extension