(a-3)x+2ay=8a-6
(a+3)x-4ay=6-10a
Multiply the first equation by 2 to get
$\displaystyle \displaystyle \begin{align*}2(a - 3)x + 4a\,y &= 16a - 12 \\ (a + 3)x - 4a\,y &= 6 - 10a \end{align*}$
and then you can subtract the second equation from the first to eliminate the $\displaystyle \displaystyle y$ variables.