Graphically this is the intersection of a parabola with a horizontal line. The solution is the two points where the line intersects the curve. Substitute for y:
3x²+12x+8=-7, 3x²+12x+15=0, x²+4x+5=0.The parabola y=3x²+12x+7 can be written:
y=3(x²+4x)+7=3(x²+4x+4-4)+7=3(x+2)²-12+7=3(x+2)²-5. The vertex is at (-2,-5) the lowest point of the parabola. So y=-8 is lower than the vertex and cannot intersect the parabola. There is no real solution, so there is probably a mistake in the question.