Is the Q2 in this diagram based on J2 and K2?
Yes, you should find Q2 and output based on J2 and K2 inputs.  It would be better to say J1=K1, which are inputs, = X which is an output from some other circuit.  To complete this you need to know that q doesn't change for jk=00.  That Q always goes to 0 for jk=01.  Q always go to 1 for jk=10.  and q goes to q* for jk=11.  You probably noticed that Q1 is changing on the 1 to 0 transition of the clock and Q2 is changing on the 0 to 1 transition.