The unit's digit of $12^{12}$ is equal to:

6

The correct answer is Option (3) → 6

To find the unit's digit of $12^{12}$, consider the pattern of unit digits of powers of 2:

$2^1 = 2$, $2^2 = 4$, $2^3 = 8$, $2^4 = 6$, $2^5 = 2$, ... (repeats every 4)

Since $12^{12}$ has the same unit digit as $2^{12}$:

$12 \mod 4 = 0$ → 12th power → corresponds to 4th in the cycle → unit digit = 6