Firstly, we need to rewrite the given equation x^(2)-6x-2y=0 in terms of y. So it becomes y=(x^2 - 6x)/2.
Then we will find the x-coordinate where the curve intersects with the line y = -4. Solving the two equations gives the value of x.
Now, we can find the area enclosed between the curve and the line by integrating the absolute value of (y + 4) from x=-4 to the intersecting point on the x-axis. The integral gives us an area of 54 square units.
To find the volume, we can use the disc method of volume calculation. It is found by the formula Volume = pi * (Area)^2. Our situation involves revolving the bounded area around the x-axis, so this method is appropriate.
So, by substituting the area value into the formula, we get Volume = pi * (54)^2.
Upon calculation, the volume is approximately 9160.88 cubic units.
This is the volume of the solid produced by the revolution of the area bounded by the curve and the line around the x-axis.