Answer
$x=0$
Work Step by Step
Using the properties of equality, the given equation, $
\dfrac{4x+2}{4}+\dfrac{3x-1}{8}=\dfrac{x+6}{16}
,$ is equivalent to
\begin{array}{l}\require{cancel}
16\left( \dfrac{4x+2}{4}+\dfrac{3x-1}{8} \right) =\left( \dfrac{x+6}{16} \right)16
\\\\
4(4x+2)+2(3x-1)=(x+6)(1)
\\\\
16x+8+6x-2=x+6
\\\\
16x+6x-x=6-8+2
\\\\
9x=0
\\\\
x=\dfrac{0}{9}
\\\\
x=0
.\end{array}
