Which is the best approach to solve Turing machines exercises? I've this exercise of which I'm not very sure about my solution.

Exercise: 


  Define the transition table about a Turing Machine that accepts words
  on the {a, b} alphabet where each a is followed by only two b.


My proposed solution is:

(f stands for transition function)


f(q0, a) = (a, q1, R)
f(q0, b) = HALT
f(q1, a) = HALT
f(q1, b) = (b, q2, R)
f(q2, a) = HALT
f(q2, b) = ACCEPT


I came up with this after thinking in the same way as finite state machines, even if I know are different with respect to Turing Machines (no tape, no reading/writing symbols and no right/left moves).

So, my question is, which is the best way of reasoning when I have to solve these kinds of problems?

Thank for your attention!
There isn't really a "best way of reasoning". Mathematical proof is essentially a creative act and there isn't a straightforward recipe you can follow. I usually find it helps to treat Turing machine construction as a programming problem, which is basically what it is.