So I included the waveform I drew in the picture. The first one is the clock pulse, the second is the output from the T-flip flop on the left, and the third is the output from the T-flip flop on the right. I'm really not sure if this is right. What I did was treated the flip flop on the right like a normal T-flip flop, toggling on a high clock pulse, and then since that output is connected to a xor whose output is connected to the other T-flip flop (I didn't know what the X meant, so I assumed it was a high) so whenever the output from the right was low the left output would toggle, and whenever the output on the right was high the left output would remain unchanged.
Can someone tell me what they think? I'm not confident about this.