Analyze the Composite Number

To check divisibility by a composite number $n$, we decompose it into factors $a$ and $b$ such that $n = a \times b$ and $\gcd(a, b) = 1$.

$12 = 2^2 \times 3$

Evaluate Option A

Factors 2 and 6 are not co-prime as they share a common factor of 2. For example, 6 is divisible by both 2 and 6, but 6 is not divisible by 12.

$\gcd(2, 6) = 2 \neq 1$

Evaluate Option B

Factors 3 and 4 are co-prime as their greatest common divisor is 1. Therefore, any number divisible by both 3 and 4 must be divisible by $3 \times 4 = 12$.

$\gcd(3, 4) = 1$

Final Verification

Since 3 and 4 satisfy the condition of being co-prime factors whose product is 12, the condition for divisibility is met.

$12 = 3 \times 4$