Analogy (number): 8 : 12 :: 6 : ____. Repair & solve: follow the same ratio as the first pair.

Introduction / Context:
This is a proportional number analogy. The original options did not include the proportional value. Applying the Recovery-First policy, we minimally repair options to make the item solvable without changing intent.

Given Data / Assumptions:

• 8 : 12 reduces to 2 : 3.
• The same ratio should apply to 6 : x.

Concept / Approach:
If 8 : 12 = 2 : 3, then multiply 6 by 3/2 to preserve proportion: x = 6 * (3/2) = 9.

Step-by-Step Solution:
Reduce first pair: 8/12 = 2/3.Apply to the second: 6/x = 2/3.Cross-multiply: 2x = 18 → x = 9.

Verification / Alternative check:
Check ratio: 6 : 9 = 2 : 3, matching the first pair.

Why Other Options Are Wrong:
8, 7, 5 do not preserve the 2 : 3 ratio.

Common Pitfalls:
Forgetting to reduce the first ratio before applying it.

Final Answer:
9.