The molecular structures of xenon compounds are determined using the Valence Shell Electron Pair Repulsion (VSEPR) theory, which considers the number of bonding pairs and lone pairs around the central xenon atom :

1. $XeF_{2}$: Xenon (Group 18) has 8 valence electrons. It forms two $\sigma$-bonds with fluorine atoms and has three lone pairs. This results in five electron domains ($sp^{3}d$ hybridisation). To minimise repulsion, the three lone pairs occupy equatorial positions, making the molecular shape linear (ii) .
2. $XeF_{4}$: Xenon forms four $\sigma$-bonds and has two lone pairs. Total electron domains = 6 ($sp^{3}d^{2}$ hybridisation). The lone pairs are positioned opposite each other in an octahedral arrangement, resulting in a square planar (i) geometry .
3. $XeO_{3}$: Xenon forms three $\sigma$-bonds (as part of double bonds) and has one lone pair. Total electron domains = 4 ($sp^{3}$ hybridisation), leading to a pyramidal (iv) structure .
4. $XeOF_{4}$: Xenon forms five $\sigma$-bonds (four with F and one with O) and has one lone pair. Total electron domains = 6 ($sp^{3}d^{2}$ hybridisation), which gives a square pyramidal (iii) geometry .

Matching these results in: (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii).