Decode the custom operator “a b ÷ c”: From the patterns 2 3 ÷ 4 = 2 and 4 4 ÷ 8 = 32, infer the rule and find the value of 6 2 ÷ 4.

Introduction / Context:
In custom-operator puzzles, juxtaposed numbers and a symbol indicate a rule you must infer from given examples. Once the rule is deduced, apply it to a new triple to compute the answer. This builds pattern recognition and abstraction skills in arithmetic.

Given Data / Assumptions:

• Examples: 2 3 ÷ 4 = 2 and 4 4 ÷ 8 = 32.
• Query: 6 2 ÷ 4 = ?
• Spacing suggests a ternary operation f(a, b, c) with the printed “÷” acting as part of the custom rule name, not ordinary division.

Concept / Approach:
Look for a simple algebraic pattern that satisfies both examples. A natural hypothesis is exponent-then-division: a^b / c.

Step-by-Step Solution:
Test a^b / c on the examples:For 2 3 ÷ 4: 2^3 / 4 = 8 / 4 = 2 ✅For 4 4 ÷ 8: 4^4 / 8 = 256 / 8 = 32 ✅Therefore the rule is consistent: f(a, b, c) = a^b / c.Apply to 6 2 ÷ 4: 6^2 / 4 = 36 / 4 = 9.

Verification / Alternative check:
Other simple interpretations (like a × b ÷ c, or (a + b) × c) fail on one of the two exemplars, so exponent-then-division is the minimal consistent rule.

Why Other Options Are Wrong:
10, 8, and 12 arise from misreading the symbol as ordinary division or using (a × b)/c or (a + b) × c, which do not fit both exemplars simultaneously.

Common Pitfalls:

• Forgetting exponent precedence and trying to distribute erroneously.
• Interpreting the printed “÷” as standard division between the second and third numbers only.

Final Answer:
9.