Explanation
1. **Identify the Domain:** The problem states that $n$ is a 'digit' and $n > 3$. As established in previous PYQs regarding the 'Nature of a Digit', this restricts $n$ to the set **{4, 5, 6, 7, 8, 9}** [12] [38].\n\n2. **Apply Constraints:**\n - Constraint A: $n$ is divisible by 3. Checking our set {4, 5, 6, 7, 8, 9}, only **6** and **9** are divisible by 3 [51].\n - Constraint B: $n$ is **not** divisible by 6. Checking our remaining candidates (6, 9):\n - 6 is divisible by 6. (Eliminated)\n - 9 is not divisible by 6. (Kept)\n - Thus, the unique value for $n$ is **9**.\n\n3. **Verify Options:** We need to find the option divisible by 4 using $n = 9$.\n - (A) $2n = 18$ (Not divisible by 4)\n - (B) $3n = 27$ (Not divisible by 4; also, since $n$ is odd, $3n$ is odd, so it can't be divisible by 4 [28])\n - (C) $2n + 4 = 22$ (Not divisible by 4)\n - (D) $3n + 1 = 3(9) + 1 = 28$. Since $28 = 7 \\times 4$, this is divisible by 4.\n\n4. **Conclusion:** Option D is the correct answer.