According to the question, In case of ${\mathrm{sp}}^3\mathrm{d}$ Hybridisation, when centre atom has one lone pair of electrons then see-saw structure is formed. In case of ${\mathrm{SF}}_4$, it has ${\mathrm{sp}}^3\mathrm{d}$ Hybridisation & one lone pair of electrons on sulphur atom. So the structure of this molecule is see-saw. 

In case of ethyne, it is first member of alkyne series. The hybridisation on triple bonded carbon atom is $\mathrm{sp}$, which has linear structure.