  Let $S \subset \mathbb P^3$ be a very general sextic surface over complex
numbers. Let $\mathcal{M}(H, c_2)$ be the moduli space of rank $2$ stable
bundles on $S$ with fixed first Chern class $H$ and second Chern class $c_2$.
In this article we study the configuration of points of certain reduced zero
dimensional subschemes on $S$ satisfying Cayley-Bacharach property, which leads
to the existence of non-trivial sections of a general memeber of the moduli
space for small $c_2$. Using this study we will make an attempt to prove
Mestrano-Simpson conjecture on the number of irreducible components of
$\mathcal{M}(H, 11)$ and prove the conjecture partially. We will also show that
$\mathcal{M}(H, c_2)$ is irreducible for $c_2 \le 10$ .
