The goal is to get same side pairs of the 6 tiles,
to fit into a $2\times 3$ grid, so that all touching sides match like so (excluding the red part), for example:
I found this by hand. I don't know if this solution is unique.
4 2 1 X 5 X 5 2 6 6 X 3 X 1 5 2 1 X 1 X 3 4 4
I'll draw a picture of it later.
There are exactly
8 solutions, or if we don't count rotations, the answer is 4 solutions, or if we count $3\times 2$ table, 16 solutions.
How did I find them?
Where are the solutions?