Solution:

The answer is $\mathbf{( E )}$. Certainly the quantity of ink will exceed triple that of 2012 for the first time in an odd year, since in even years it decreases. If $2k+1$ years have passed, then, it will have become
$$\frac{3}{2} \cdot \left(\frac{5}{6} \cdot \frac{3}{2}\right)^{k}.$$
Requiring that this quantity be greater than $3$, after a few simple steps we find ourselves having to find the minimum $k$ for which
$$\left(\frac{5}{4}\right)^{k} > 2$$
but for $k=3$ we get $\frac{125}{64} < \frac{128}{64} = 2$, while for $k=4$ we find $\frac{625}{256}$ which is clearly greater than $2$. We will then be in the $2 \cdot 4 + 1$-th year, that is, the ninth.