Okay, for one, it's spelled symmetry.
In some cases, a Hexagon may have none, but assuming you mean a regular Hexagon, it would have six lines of symmetry. Hope I help. Sorry for criticizing your spelling, kind of a pet peeve >.<
(P.S. You better not use this for homework!)
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6 lines of symmetry for a 2-d hexagon
A regular 6 sided hexagon has 6 lines of symmetry
2 parallel lines * * * * * The above answer is not wholly correct. A hexagon can have one, two or three pairs of parallel lines: a regular hexagon has 3 pairs.
36
There are 6 lines of symmetry in a hexagon.