Restriction and re-labeling on CCS
I am not completely sure about what is causing your confusion, but perhaps this can help:

$a.\bar{b}.0$ can only perform $a$.

$(a.\bar{b}.0)\setminus\{b\}$ can only perform $a$.

$((a.\bar{b}.0)\setminus\{b\})[a\to b]$ can only perform $b$ (i.e. $a$ after substitution).

The full process $((a.\bar{b}.0)\setminus\{b\})[a\to b]\mid(\bar{b}.b.0)+\bar{b}.c.0$ can perform $b$, $\bar b$ (two distinct ways), and $\tau$ (two distinct ways).

Also note that the unrelated process $((a.\bar{b}.0)[a\to b])\setminus\{b\}$ would instead be stuck.