Let $F$ be a closed surface. If $i,i':F\to\E$ are two regularly homotopic generic immersions, then it has been shown in [N] that all generic regular homotopies between $i$ and $i'$ have the same number mod 2 of quadruple points. We denote this number by $Q(i,i')\in\C$. For $F$ orientable we show that for any generic immersion $i:F\to\E$ and any diffeomorphism $h:F\to F$ such that $i$ and $i\circ h$ are regularly homotopic, $$Q(i,i\circ h)=\bigg(\r(h_*-\Id)+(n+1)\ep(h)\bigg)\bmod{2},$$ where $h_*$ is the map induced by $h$ on $H_1(F,\C)$, $n$ is the genus of $F$ and $\ep(h)$ is 0 or 1 according to whether $h$ is orientation preserving or reversing, respectively.\\ \phantom{aa} We then give an explicit formula for $Q(e,e')$ for any two regularly homotopic embeddings $e,e':F\to\E$. The formula is in terms of homological data extracted from the two embeddings.