1. Let's clarify the problem: We want to understand why point E lies on line AGE implies a certain value, here 12. 2. "E lies on AGE" means points A, G, and E are collinear. 3. If we have a segment or line AGE, and E is on it, then the distances satisfy the segment addition postulate: $$AG + GE = AE$$. 4. Suppose from the problem context, the length of AE is given or calculated as 12. 5. Therefore, if E lies on AGE, the sum of the lengths AG and GE must equal 12. 6. This is the logical jump: from E lying on AGE, we deduce $$AG + GE = AE = 12$$. 7. Hence, the value 12 comes from the total length of segment AE, which E divides into parts AG and GE. 8. This is a fundamental property of points on a line segment, ensuring the sum of parts equals the whole. Final answer: The jump to 12 comes from the segment addition postulate applied to points A, G, and E on the same line, where $$AE = 12$$.