The hint they gave you is a good one. x is equal to "8 - 2y", which is already half-solved for us. Take your second equation, and replace the "x" variable with what it's equal to:
y - x = 4
y - (8 - 2y) = 4
y - 8 + 2y = 4
y + 2y = 8 + 4
3y = 12
y = 4
Now that we know the exact number for y, we can plug this back into our first equation:
x = 8 - 2(4)
x = 8 - 8
x = 0
You always want to check your answers to make sure they're right. If y = 4 and x = 0, then....
y - x = 4
(4) - (0) = 4
4 - 0 = 4
This checks out!
Use this method to try your second one :)