#### Answer

The solution is $m=3$

#### Work Step by Step

$\dfrac{2m}{m-2}-\dfrac{6}{m}=\dfrac{12}{m^{2}-2m}$
Take out common factor $m$ from the denominator of the fraction on the right side of the equation:
$\dfrac{2m}{m-2}-\dfrac{6}{m}=\dfrac{12}{m(m-2)}$
Multiply the whole equation by $m(m-2)$
$m(m-2)\Big[\dfrac{2m}{m-2}-\dfrac{6}{m}=\dfrac{12}{m(m-2)}\Big]$
$2m(m)-6(m-2)=12$
$2m^{2}-6m+12=12$
Eliminate $12$ from both sides:
$2m^{2}-6m=0$
Take out common factor $2m$ from the left side:
$2m(m-3)=0$
Set both factors equal to $0$ and solve each individual equation for $m$:
$2m=0$
$m=\dfrac{0}{2}$
$m=0$
$m-3=0$
$m=3$
The original equation is undefined for $m=0$, so the solution is only $m=3$