Conjugacy and the Class Equation · Challenge problem

$Q_8\times\mathbb{Z}_3$ has order $24$. Using that conjugacy classes of a direct product are products of the factors' own classes ($\operatorname{cl}_{G\times H}(g,h)=\operatorname{cl}_G(g)\times\operatorname{cl}_H(h)$, since $(a,b)(g,h)(a,b)^{-1}=(aga^{-1},bhb^{-1})$), how many conjugacy classes does $Q_8\times\mathbb{Z}_3$ have in total?