  For a Calabi-Yau 3-fold $X$, we explicitly compute the Donaldson-Thomas type
invariant counting pairs $(F, V)$, where $F$ is a zero-dimensional coherent
sheaf on $X$ and $V\subset F$ is a two dimensional linear subspace, which
satisfy a certain stability condition. This is a rank two version of the
DT-invariant of rank one, studied by Li, Behrend-Fantechi and
Levine-Pandharipande. We use the wall-crossing formula of DT-invariants
established by Joyce-Song, Kontsevich-Soibelman.
