Both expressions are equal to Y, so set them equal to each other and solve for x.
Set both equations equal to each other:
2x + 2 = -(1/3)x + 2(2/3)
Collect the x's on one side, and the constants on the other. To keep the equation equal, if you subtract or add something from/to one side of the equation you have to do it to the other:
2x + (1/3)x = 2(2/3) - 2
Multiply out the 2(2/3):
2x + (1/3)x = (4/3) - 2
Re-express everything in terms of thirds so we can add/subtract them easily.
(6/3)x + (1/3)x = (4/3) - (6/3)
(7/3)x = -(2/3)
Divide both sides of the equation by 7/3 to get x:
x = -(2/7)