x=y^2+8y+16-4=(y+4)^2-4; (x+4)=(y+4)^2 is another way of expressing this sideways parabola, so that its vertex becomes apparent: (-4,-4). The parabola's arms are to the right and are symmetrical about the line y=-4. The x intercept (y=0) is 12. The y intercepts (x=0) are when y+4=±2, so y=-2 and -6, which are equidistant from the axis y=-4. These details should help in plotting the graph: the position of the three intercepts and the position of the vertex.
The first thing to do is to draw the axis, y=-4, parallel and below the x axis. Mark the vertex at (-4,-4), and show the axis intercepts at x=12 and y=-2 and -6. The parabola is symmetrical about the axis y=-4.