Yes, there is a way within a theoretical framework. Count all of the electrons, etc..., create your Lewis structure, and then count the number of electron domains, from there you'd get your molecular geometry. Within this case, there is a lone pair of electrons on the tin atom, but it is also a tetrahedral molecule (electron-pair geometry), however, its molecular geometry is trigonal pyramidal, so the hybridization for tetrahedral generally is sp^3.
Sometimes, for instance in general chemistry, or organic chemistry, you can get the hybridization on that alone, however, there are instances where a molecules geometry won't exactly match up to its hybridization so knowing how to draw and deduce the sigma/pi - bonds, and knowings vesper theory would be more paramount than simply going on the "status-quo" so to speak. But within his course and this question, it is simply trying to test him on a more basic level of understanding.