if both segments are parallel to each other, that means both segments have the same slope value, thus
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ -3}}\quad ,&{{ y}})\quad
% (c,d)
B&({{ 6}}\quad ,&{{ -4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-y}{6-(-3)}\implies \cfrac{-4-y}{6+3}
\\\\\\
\boxed{\cfrac{-4-y}{9}}[/tex]
[tex]\bf -------------------------------\\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
C&({{ 7}}\quad ,&{{ 6}})\quad
% (c,d)
D&({{ -2}}\quad ,&{{ 8}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{8-6}{-2-7}\implies \boxed{\cfrac{2}{-9}}\\\\
-------------------------------\\\\
\cfrac{-4-y}{9}=\cfrac{2}{-9}\implies -4-y=\cfrac{2\cdot 9}{-9}\implies -4-y=\cfrac{2}{-1}
\\\\\\
-4-y=-2\implies -4+2=y\implies -2=y[/tex]
