#### Answer

$x=\left\{ \dfrac{1}{2},\dfrac{3}{2} \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|4-4x|+2=4
,$ use the properties of equality to isolate the absolute value expression. Then use the properties of absolute value equality.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
|4-4x|=4-2
\\\\
|4-4x|=2
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
4-4x=2
\\\\\text{OR}\\\\
4-4x=-2
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
4-4x=2
\\\\
-4x=2-4
\\\\
-4x=-2
\\\\
x=\dfrac{-2}{-4}
\\\\
x=\dfrac{1}{2}
\\\\\text{OR}\\\\
4-4x=-2
\\\\
-4x=-2-4
\\\\
-4x=-6
\\\\
x=\dfrac{-6}{-4}
\\\\
x=\dfrac{3}{2}
.\end{array}
Hence, $
x=\left\{ \dfrac{1}{2},\dfrac{3}{2} \right\}
.$