I get a little giddy when talking about weird molecules like xenon difluoride — it totally breaks the simple ‘octet-only’ story we learn first. Start by counting valence electrons: xenon brings 8, each fluorine brings 7, so 8 + 2×7 = 22 valence electrons. If you draw two Xe–F single bonds that uses 4 electrons,
leaving 18 to place as lone pairs. Each fluorine needs three lone pairs to complete its octet (that’s 12 electrons), leaving 6 electrons or three lone pairs sitting on xenon. So the Lewis picture has two bonding pairs and three lone pairs on Xe, giving xenon five electron domains and, yes, ten electrons around Xe — an expanded octet rather than an octet-limited atom.
Turning to geometry, VSEPR predicts shapes from electron domains. Five domains correspond to a trigonal bipyramidal electron geometry. Lone pairs prefer the equatorial positions because equatorial positions have two 90° neighbors and one 180°, while axial positions have three 90° neighbors — placing the three lone pairs equatorially minimizes lone pair–lone pair and lone pair–bond pair repulsions. That forces the two fluorines into the axial sites, opposite each other, producing a linear molecular shape with a 180° F–Xe–F angle.
If you want a more modern bonding picture, chemists often invoke a three-center four-electron (3c–4e) model for the linear axis: the three atoms share a set of
orbitals so the electrons are delocalized over F–Xe–F, which fits the observed bond lengths and explains stability without relying heavily on invoking d-orbital participation. Formal charges work out nicely (all atoms formally neutral in the simple Lewis assignment), and the strong electronegativity of fluorine gives the bonds significant ionic character. I find the way simple counting, geometry, and a touch of MO thinking
come together pretty satisfying.