It is possible for a hexagon to have one pair of parallel sides. A hexagon can have 0, 1, 2 or 3 pairs of parallel sides, and can have 0, 2, 3, 4, 5, or 6 parallel sides.
a hexagon
A hexagon can have 0, 1, 2 or 3 pairs of parallel sides. A regular hexagon has 3 pairs of parallel sides. A hexagon can also have 2 sets of 3 parallel sides! If you are allowed to count sides in more than one pair, this would be 6 pairs of parallel sides!
An irregular hexagon.
A hexagon with only one pair of parellel sides
A regular hexagon has three pairs of parallel sides. An irregular hexagon can have two, one or none.
One pair? If it is one pair of parallel sides, then it is a trapezoid. If it has 2 pairs of parallel sides, then it is a parallelogram.
In a regular hexagon, all sides are parallel to the one across from it. In other hexagons, this need not be the case.
A trapezium.
RHOMBOID
A quadrilateral that has only one pair of parallel sides (the other pair not parallel) is a trapezium.
An irregular hexagon.