Since this is a homework question, I'll give hints rather than a numerical answer.
Clipping a convex polygon
Think about how many times the polygon can cross each edge of the rectangle. In general, a polygon can cross one of the edges of the rectangle an arbitrarily large number of times. How is this number reduced if the polygon is convex?
This will give you the maximal number of new angles that can be added per rectangle edge, which should lead you to the answer.
Clipping a non-convex polygon
As for your guess of 2n, even for a non-convex polygon it may not be able to reach this high. If one vertex is outside the rectangle, then in order to create 2 new vertices both of its neighbouring vertices must be inside the rectangle. This means you cannot create 2n new vertices this way.
The exception is when an edge of the polygon crosses 2 edges of the rectangle, for example at a corner of the rectangle. This allows creating two new vertices from a single edge. So for small enough n, it is possible to clip to a polygon with 2n vertices, but for larger n this is not possible.