\(\dfrac{x-2}{6}=2x-1+\dfrac{2x-1}{3}\)
=>\(\dfrac{x-2}{6}=\dfrac{3\left(2x-1\right)+\left(2x-1\right)}{3}\)
=>\(\dfrac{x-2}{6}=\dfrac{4\left(2x-1\right)}{3}\)
=>\(\dfrac{x-2}{6}=\dfrac{8\left(2x-1\right)}{6}\)
=>8(2x-1)=x-2
=>16x-8=x-2
=>15x=6
=>\(x=\dfrac{6}{15}=\dfrac{2}{5}\)