How do I implement a simple finite state machine with 2 T flip-flops?
This looks like a homework question, which I won't answer.  But here are some pointers:


You cannot represent more states than what you have available -> that means that you will have to go to the next higher state (i.e. 2 FF's for 4 states) or use only one FF per state. (i.e. FF #1 correlates directly to A).
option #1 ( 2 FF's and 4 states) is more economical but you have to make sure that the unused state does n't not get activated and then locks out.


you might draw this as a 4th state "D" with loops back to itself.
what is generally considered safe design is that you always have explicit transitions AWAY from the unused state in case it gets activated.

option #2 uses more FF's but cannot have any hidden states.


it is inherently safer.
it is known as a "one hot" design and thermometer codes are examples of this.



Your choice of states "A = 00" etc. will make the design simpler or more complicated.  SO may want to go with what you decribe or you may want to go with state C = "10".  You should look at all possibilities.

The first SM, only uses 0 or 1 as an input because it only has one input variable.  They should have used a variable for clarity anyways.  You'll notice in the table that it is marked as "x" but not in the diagram.