Answer
$n=-1$.
Work Step by Step
The given points are
$(x_1,y_1)=(n,6)$ and $(x_2,y_2)=(1,2)$
Slope $m_1=\frac{y_2-y_1}{x_2-x_1}$.
Substitute all values.
Slope $m_1=\frac{2-6}{1-n}=\frac{-4}{1-n}$.
The given equation of the parallel line:
$2x+y=3$
The slope intercept form is
$y=-2x+3$.
Slope $m_2=-2$.
Equate both slopes.
$\Rightarrow m_2=m_1$
Substitute both values.
$\Rightarrow -2=\frac{2-6}{1-n}$
Multiply the equation by $(1-n)$.
$\Rightarrow -2\cdot (1-n)=\frac{-4}{1-n}\cdot (1-n)$
Simplify.
$\Rightarrow -2+2n=-4$
Add $2$ to both sides.
$\Rightarrow -2+2n+2=-4+2$
Simplify.
$\Rightarrow 2n=-2$
Divide both sides by $2$.
$\Rightarrow \frac{2n}{2}=\frac{-2}{2}$
Simplify.
$\Rightarrow n=-1$.
