Right excuse the quick paint job but here's an idea.
This is what i normally do given these probs (our lecturer advised us to do them this way!)
In the first diagram the red lines are y's perm, the black lines are x's perm.
Then just fill in lines so that the everthing goes to its right place. (example shown in the second diagram).
So my z would be (1)(2 3)(4)(5)(6). But there could be more than one way of doing it.