There is a long way - but I like the short way!
There is only one correct solution so why not start with A. & D. (the easy answers) and plug them in for your variables and test them.
I started with A and what do you know - it checks out!
{5x+4y=-14} Put -6 in for x and 4 in for y
-30 + 16 = -14 Is that right? Yes Now try the next equation.
{3x+6y=6} Put -6 in for x and 4 in for y
-18 + 24 = 6 Is that right? Yes. We are good. Problem solved.
The long way would be to use the substitution method and solve for x and then substitute to find y.