I pretty much know this problem

4y+2x=18
3x+6y=26
multiply -3= -6x+-12y= -54
multiply 2 = 6x+-12= 52
The answer is -2 but I am not sure what to do next since both x and y were canceled out.

When you multiplied the second equation by 2 your result is wrong.

It should be: 6x + 12y=52
NOT: 6x-12y=52

2x+4y=18

3x+6y=26
Notice I changed to order in the top equation.

Your equations are parallel lines, no solutions

To solve the system of equations:

4y + 2x = 18 ...(Equation 1)
3x + 6y = 26 ...(Equation 2)

First, let's rearrange Equation 1 to solve for x:
2x = 18 - 4y
x = (18 - 4y)/2
x = 9 - 2y ...(Equation 3)

Now, let's substitute Equation 3 into Equation 2:
3(9 - 2y) + 6y = 26
27 - 6y + 6y = 26
27 = 26

At this point, you noticed that both x and y were canceled out, which means that the system of equations is inconsistent, and there is no unique solution. In other words, there is no combination of x and y that satisfies both equations simultaneously.

Therefore, the system of equations is said to be inconsistent and has no solution. This explains why you couldn't find a numerical value for x and y.