Intro Calculus question. I've taken this course (twice, lol) and I'm trying to help my nephew but cant!?

I can't remember how to do this seemingly simple calculus question. I promised I would have it sorted it out by tomorrow morning for my nephew, and it's getting a little late. Any help would be greatly appreciated. The question: A spaceship is flying along the line y = 3x^3 - 8x. At point P the ship turns off it's power and changes direction. The line that pes through point P must also p through the point (4,0). I'm guessing point P is a point of the tangent line (to the curve represented by the equation) and thus the derivative of the initial equation is the slope of that tangent line. What are the coordinates of point P (x,y). More importantly, how do I go about solving this. PLEASE HELP. Big Points!