A state $q_{xy}$ means $n_a \mod \ 2 =x$ , $n_b \mod \ 3=y$
$q_{00}$ means $n_a \mod \ 2 =0,n_b \mod \ 3=0$ [no of $a\text{’}$s is divisible by $2$ and no of $b\text{’}$s is divisible by $3$]
$q_{00} \times a \rightarrow q_{10}$
$q_{00} \times b \rightarrow q_{01}$ and so on.