#### Answer

$x=\left\{ 0,6 \right\}$

#### Work Step by Step

Changing to exponential form, the given equation, $
\log_2(x-4)(x-2)=3
,$ is equivalent to
\begin{array}{l}\require{cancel}
(x-4)(x-2)=2^3
\\\\
(x-4)(x-2)=8
.\end{array}
Using the concepts of solving quadratic equations, then
\begin{array}{l}\require{cancel}
x(x)+x(-2)-4(x)-4(-2)=8
\\\\
x^2-2x-4x+8=8
\\\\
x^2-2x-4x=8-8
\\\\
x^2-6x=0
\\\\
x(x-6)=0
.\end{array}
Equating each factor to $0$ and solving for the variable, the solutions are $
x=\left\{ 0,6 \right\}
.$
Upon checking, $
x=\left\{ 0,6 \right\}
$ satisfy the original equation.