\[\frac{3x + 2}{12} - \frac{x - 4}{8} = 2\ \ \ \ \ \ \ \ | \cdot 24\]
\[2 \cdot (3x + 2) - 3 \cdot (x - 4) = 48\]
\[6x + 4 - 3x + 12 = 48\]
\[3x = 48 - 16\]
\[3x = 32\]
\[x = 10\frac{2}{3}.\]