\(\dfrac{3x-4}{4}=\dfrac{4x-8}{5}\)
\(\Leftrightarrow\dfrac{3x-4}{4}-\dfrac{4x-8}{5}=0\)
\(\Leftrightarrow\dfrac{5\left(3x-4\right)}{20}-\dfrac{4\left(4x-8\right)}{20}=0\)
\(\Leftrightarrow\dfrac{15x-20}{20}-\dfrac{16x-32}{20}=0\)
\(\Leftrightarrow\dfrac{15x-20-16x+32}{20}=0\)
\(\Leftrightarrow\dfrac{x-12}{20}=0\)
\(\Leftrightarrow x-12=0\)
\(\Leftrightarrow x=12\)