Given that n is a digit greater than 3, divisible by 3 but not divisible by 6, let $n=9$. Now, let's check the options: $2n=2 \times 9=18$, which is not divisible by 4. (b) $3n=3 \times 9=27$, which is not divisible by 4. (c) $2n+4=2 \times 9+4=22$, which is not divisible by 4. (d) $3n+1=3 \times 9+1=28$, which is divisible by 4.