you forgot that 6y  (6y) = 12y. so it would be:
5x+6y=23

4x6y= 14

x + 12y = 37
instead, try adding the equations together
5x+6y=23
+
4x6y= 14

9x + 0 = 9
5x+6y=23
4x6y=14
I've tried it:
5x+6y=23

4x6y= 14
_______________
x = 37
Then I did this:
5(37)+6y=23
185+6y=23
185 185
6y=162
 
6 6
y = 27
But when I plug those numbers in, it doesn't work. Help please
P.S.: I am not looking for the answer, but for the way of answering this question. Thank you