A parallelogram is by definition made of two pairs of parallel lines; it is always a four sided figure. A hexagon is a six sided figure, so it cannot be a parallelogram.
It depends on the type of parallelogram:The classic generic-looking parallelogram, having no right angles, and having adjacent sides of unequal length, has no lines of symmetry (only point symmetry about the point of intersection of the diagonals).Special types of parallelograms are as follows:A square has 4 lines of symmetry: horizontal, vertical, and one containing each diagonal.A non-square rhombus has two lines of symmetry: one containing each diagonal.A non-square rectangle has two lines of symmetry: horizontal and vertical.