\(\frac{3x+2}{2}-\frac{3x+1}{6}=2x+\frac{5}{3}\)
\(\Leftrightarrow\frac{3\left(3x+2\right)}{6}-\frac{3x+1}{6}=\frac{6x+5}{3}\)
\(\Leftrightarrow\frac{9x+6-3x-1}{6}=\frac{6x+5}{3}\)
\(\Leftrightarrow6x+5=12x+10\)
\(\Leftrightarrow6x=-5\Leftrightarrow x=-\frac{5}{6}\)