What is the remainder if 2^192 is divided by 6?

When I see a huge number like $2^{192}$, I recall the concept of 'Strategic Intimidation Management' from PYQ analysis [7]. The examiner doesn't want me to calculate this; they want me to find a pattern (Cyclicity) [1].\n\nLet's try small powers of 2 and divide them by 6 to see what happens:\n\n1. Take $2^1 = 2$. Divide by 6. Remainder is **2**.\n2. Take $2^2 = 4$. Divide by 6. Remainder is **4**.\n3. Take $2^3 = 8$. Divide by 6 (6 goes into 8 once, leaving 2). Remainder is **2**.\n4. Take $2^4 = 16$. Divide by 6 (6 goes into 16 twice, 6x2=12, leaving 4). Remainder is **4**.\n\nI see a clear alternating pattern here, similar to unit digit patterns in previous years [29]:\n- If the power is **Odd** (1, 3, 5...), the remainder is 2.\n- If the power is **Even** (2, 4, 6...), the remainder is 4.\n\nThe question asks for $2^{192}$.\nSince 192 is an **Even** number, the remainder must be **4**.