A quadrilateral with no sides parallel and diagonals that are perpendicular Options:
Quadrilateral
Kite
Trapezoid
Isosceles Trapezoid
Parallelogram
Rectangle
Rhombus
Square

Explanation:

Of your original given list, let's write down the parallelograms. They are:

So we cross those off the list since we want a quadrilateral with no sides parallel. A parallelogram, by definition, is a quadrilateral with both pairs of opposite sides that are parallel.

We can also rule out the trapezoids because a trapezoid is a four sided figure (quadrilateral) where we have exactly 1 pair of parallel sides, while the other sides are not parallel.

Lastly, we can rule out the kite because any kite has perpendicular diagonals.

The only thing left is quadrilateral. In my opinion this answer should be more specific and say "quadrilateral that isn't a parallelogram, a trapezoid, or a kite", but I think I see what your teacher was going for here.

ou would have 12 of each