First, your answer is right, though it should be written as [imath]\pm(6x+1)[/imath] to make it clear that both signs must be the same. In the graph below, the solid red and green lines are your tangents, and the dotted lines are theirs:
Clearly their lines don't both pass through the given point. So they've made a mistake, at least a typo.
As for your work, I don't know what you're doing. What does p mean, as you have been taught? Where does "p = 2kn" come from? (I would be using the derivative, but perhaps you haven't learned that, and this is a special formula you learned for the parabola.)