Well, once again, I recommend getting started by drawing the finite state machine.

So on a or on b, we go over to state 2,

and we could end there because this is optional,

or on c or d, we could go to state 3 and end there.

Here at the top, I've encoded the edges from state 1 on a we go to state 2.

From state 1 on b, we go to state 2 as well--a or b.

From state 2 on c, we go to state 3.

From state 2 on d, we go to state 3.

And both states, 2 and 3, are accepting.

Then down here, I have 3 test cases.

"ac" which should be accepted.

"aX" which should not. X has no business in this regular expression.

And just "b" alone, which should be fine because the c - d part is optional.

Let's go see.

And we get exactly the output we were expecting--true, false, true.

Now you might have been tempted to have a c - d self-loop back to 2,

instead of this right-hand side of the finite state machine.

However, this self-loop changes the meaning to "[a - b][c - d]*".

If you have this self-loop, acc is accepted--a-c-c, and it shouldn't be,

so the self-loop is not the right way to go.