The unit digit of 12^12 is:

The correct answer is Option (4) → 6

The unit digit of \(12^{n}\) is the unit digit of \(2^{n}\). The unit digits of powers of 2 repeat in a cycle of 4:

    \(2^1 \to 2,\quad 2^2 \to 4,\quad 2^3 \to 8,\quad 2^4 \to 6\)

Since 12 is a multiple of 4, \(2^{12}\) is at the end of a cycle:

    \(12 = 4 \times 3\)
    \(2^{12} = (2^4)^3\), whose unit digit is that of \(6^3\), that is 6

So the unit digit of \(12^{12}\) is 6.