Your first mistake is that you made an arithmetic error in solving for x. 12/4= 3, not 4! which is a parabola with x- axis as axis of symmmetry, vertex at (-3, 0), and opening to the right. The line x= y is always the left boundary and the parabola the right boundary of the area they define so you want to subtract the x value of the line from the x value of the parabola to get a positive value: .
Yes, one of the points of intersection is to the left of the y-axis and one to the right but that is not really relevant. What are the y coordinates of those points. You want to integrate where is the y coordinate of the lower point and is the y coordinate of the higher point.