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\(\frac{x-2}{2}+\frac{x-2}{3}+\frac{x-2}{6}=2\)
\(\Leftrightarrow\frac{3\left(x-2\right)}{6}+\frac{2\left(x-2\right)}{6}+\frac{x-2}{6}=\frac{12}{6}\)
\(\Leftrightarrow3\left(x-2\right)+2\left(x-2\right)+\left(x-2\right)=12\)
\(\Leftrightarrow3x-6+2x-4+x-2=12\)
\(\Leftrightarrow6x=12\)
\(\Leftrightarrow x=2\)
\(\frac{x-2}{2}+\frac{x-2}{3}+\frac{x-2}{6}=2\)
\(\frac{3x-6}{6}+\frac{2x-4}{6}+\frac{x-2}{6}=\frac{12}{6}\)
\(3x-6+2x-4+x-2=12\)
\(6x-12=12\)
\(6x=24\Leftrightarrow x=4\)