Permutation Combinations Mobile Pattern Codes [closed]

Please help write codes to determine 4 to 6 dot patterns. I am stuck after permutations input. It would really help if one could write direct so I could copy paste code to determine list of 4 to 6 dot patterns. Pl refer article.

https://www.guokr.com/article/49408/ I have uploaded jpeg of the error I am facing Code error at =Flatten[{#, Reverse@#} & /@ Partition[{1, 3, 4, 6, 7, 9, 1, 7, 2, 8, 3, 9, 1, 9, 3, 7}, 2], 1]