Question:
A sequential circuits has one input(X) and two ouputs(Z1 and Z2). An output Z1=1 occurs every time the input sequence 010 is complete, provided that the sequence 100 has never occurred. An output Z2=1 output has occurred, Z1= can never occur but not vice versa. Find a Mealy state graph and state table.

Can I get help getting the right path to start.

 

here you go, although I am sure they had already covered this in class >>> http://en.wikipedia.org/wiki/State_diagram

 

You can also check this tutorial:
http://www.allaboutcircuits.com/vol_4/chpt_11/5.html

Your extra restriction can be implemented using the reset pin of the Flip Flops.