Six times a number x, plus 4 times a number y, equals 14. negative eight times x minus 4 times y equals -12. what are the numbers?

Converting this into an equation, we get:
6x+4y=14
-8x-4y=-12

We can solve this by adding the system of equations.

       6x+4y=14
 +   -8x-4y=-12

      -2x=2

Simplifying, we get that x=-1. We can replug this into one of the equations to get y. We'll choose 6x+4y=14

Plugging in -1 for x, we get that:
6(-1)+4y=14
which is
-6+4y=14
which is
4y=20

Simplify this to get that y=5

To check, you can plug in x and y into both equations to make sure that they are true.

6(-1)+4(5)=14
-6+20=14
14=14 which is true

-8(-1)-4(5)=-12
8-20=-12
-12=-12 which is true

x=-1 and y=5

:)