well, a line parallel to another, will have the same slope as the other, therefore, if this line is parallel to 4x-2y+6=0, then it must have the same slope, so, hmmm what is it anyway?
well, let's solve 4x-2y+6=0 for "y".
[tex]\bf 4x-2y+6=0\implies 4x+6=2y\implies \cfrac{4x+6}{2}=y
\\\\\\
\cfrac{4x}{2}+\cfrac{6}{2}=y\implies \stackrel{slope}{2}x+3=y[/tex]
so, notice, the equation now in slope-intercept form, we can see what its slope is, alrite. So we're looking for a line whose slope is 2 and goes through 4,6.
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 4}}\quad ,&{{ 6}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-6=2(x-4)
\\\\\\
y-6=2x-8\implies y=2x-2[/tex]
