Square, Rectangle.
When they are evenly spaced they are parallel...SYMMETRICAL.
A shape with two pairs of parallel sides is ........ a parallelogram!
It will, unless the shape is symmetrical and the axis of reflection is parallel to the axis of symmetry.
An equilateral hexagon would work. It has more than 2 pairs of parallel sides though. There is no shape with only 2 pairs of parallel sides besides a parallelogram.
A cone
parallelogram
A triangle.
A parallelepiped.
It can have anywhere between 0 and 12 pairs of parallel sides.
trapezium
rhombus