To solve this problem, we need to determine the molecular geometry of each compound in List I and match it with the correct geometry in List II. Let's analyze each compound:$\newline •$A. $$NH$_3: \\$Ammonia (NH$_3$) has a central nitrogen atom with three hydrogen atoms and one lone pair.$\\$The electron pair geometry is tetrahedral, but due to the lone pair, the molecular geometry is trigonal pyramidal.$\\$Thus, NH$_3$ corresponds to I. Trigonal Pyramidal.$\\ •$B. $$BrF$_5: \\$Bromine pentafluoride (BrF$_5$) has a central bromine atom with five fluorine atoms and one lone pair.$\\$The electron pair geometry is octahedral, but the presence of one lone pair makes the molecular geometry square pyramidal.$\\$Thus, BrF$_5$ corresponds to IV. Square Pyramidal.$\\ •$C. $$XeF$_4: \\$Xenon tetrafluoride (XeF$_4$) has a central xenon atom with four fluorine atoms and two lone pairs.$\\$The electron pair geometry is octahedral, but the molecular geometry is square planar due to the two lone pairs.$\\$Thus, XeF$_4$ corresponds to II. Square Planar.$\\ •$D. $$SF$_6: \\$Sulfur hexafluoride (SF$_6$) has a central sulfur atom with six fluorine atoms and no lone pairs.$\\$The electron pair geometry and molecular geometry are both octahedral.$\\$Thus, SF$_6$ corresponds to III. Octahedral.$\\$Based on the analysis, the correct matches are:$\\$A$\to$I, B$\to$IV, C$\to$II, D$\to$III.$\\$Therefore, the correct option is Option 3.