Single-molecule conductance measurements have focused primarily on organic molecular systems. Here, we carry out scanning tunneling microscope-based break-junction measurements on a series of metal chalcogenide Co6Se8 clusters capped with conducting ligands of varying lengths. We compare these measurements with those of individual free ligands and find that the conductance of these clusters and the free ligands have different decay constants with increasing ligand length. We also show, through measurements in two different solvents, 1-bromonaphthalene and 1,2,4-trichlorobenzene, that the conductance decay of the clusters depends on the solvent environment. We discuss several mechanisms to explain our observations.