Case 1:
Push 1, pop 1
push 2, pop 2
push 3, pop 3
Case 2:
push 1
Push 2, Pop 2
Pop 1
push 3, pop 3
As we can see there 2 possibilities before 3(1, 2 and 2, 1), and there will be 4 possibilities after 3 (456, 546, and 564, 654,465).
so far we got 10 sequences.
Remaining 16 will be as follows:
4 5 3 2 1 6
4 5 3 2 6 1
4 5 3 6 2 1
5 4 3 2 6 1
5 4 3 6 2 1
5 4 3 2 1 6
143256
143265
143526
143562
143652
243156
243165
243516
243561
243651
Hence, there total 26 sequences possible.