I don't think it matters what variable to integrate with respect to, I would choose x in this case.
Finding the intersections between the fuctions is the first thing I would do.
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region
y=3x^2, y=8x^2, 4x+y=4, x greater than or equal to 0.