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Calculate the number of 
subsets and proper subsets for the following set:
{x / x is a side of a hexagon}
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Notice I fixed one obvious typo in your post.
Next time please be more attentive . . . in order for we take you seriously . . .
Solution
Hexagon has 6 (six) sides, so the original set has 6 elements {a, b, c, d, e, f}, where I used 6 first letters
of English alphabet to denote the sides.
The number of all subsets of this original set is 
= 64, including the empty set and the improper subset.
Improper subset is the set coinciding with the original subset.
All other subsets are proper subsets.
So, there are 64 subsets in all, and 63 proper subsets.
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See the lesson
- How many subsets are there in a given finite set of n elements?
in this site.
