Decode the pattern — 4 − 4 = 12, 6 − 6 = 30, 2 − 2 = 2. Compute 8 − 8.

Introduction / Context:These are not real subtractions; the symbol “−” encodes a number-to-number mapping. We must infer a single rule consistent with all given examples and apply it to 8 − 8.

Given Data / Assumptions:

• 4 − 4 = 12
• 6 − 6 = 30
• 2 − 2 = 2

Concept / Approach:Try simple expressions in n such as n^2 ± n or linear forms. Observing: 4 → 12 suggests 4^2 − 4 = 12; 6 → 30 suggests 6^2 − 6 = 30; 2 → 2 suggests 2^2 − 2 = 2. Hence the rule fits all: f(n) = n^2 − n.

Step-by-Step Solution:

Verification / Alternative check:Check the rule on all given examples to confirm consistency (it matches all three).

Why Other Options Are Wrong:

• 8, 16, 38 do not follow the deduced quadratic rule.

Common Pitfalls:

• Assuming real subtraction instead of a coded pattern.

Final Answer:56