Counting number of states from a regular expression
The rule for the $\sigma\in \Sigma$ must be applied each time a letter appears in the regular expression, not only once per letter : you must build a different automata each time the letter appears. If you see it as some kind of digital circuit, you do not want to use the circuit that recognizes $a$ in $ab$ for the circuit that recognizes $a$ in $a + \epsilon$.

So you have five letters that appear in $r$, that's $5*2$ states. Then you have 2 concatenations, two unions and two stars. That's $2 * 0 + 2*2+2*2 = 4*2$ states.