To determine which molecule has the maximum dipole moment, we need to analyze the molecular geometry and the electronegativity differences between the atoms.$\\$Let's consider each option:$\\$• $$CO$_2: \\$The molecule is linear with oxygen atoms on both sides of the carbon atom.$\\$The dipoles from the C=O bonds cancel each other out, resulting in a net dipole moment of zero.$\\$• $$CH$_4: \\$Methane is a tetrahedral molecule with four equivalent C-H bonds.$\\$The dipoles cancel out due to symmetry, resulting in a net dipole moment of zero.$\\$• $$NH$_3: \\$Ammonia has a trigonal pyramidal shape with a lone pair on the nitrogen atom.$\\$The N-H bonds create a net dipole moment pointing towards the nitrogen,$\\$resulting in a significant dipole moment.$\\$• $$NF$_3: \\$Nitrogen trifluoride also has a trigonal pyramidal shape, similar to ammonia.$\\$However, the electronegativity of fluorine is higher than that of nitrogen,$\\$causing the dipole moment to point towards the fluorine atoms.$\\$This results in a smaller net dipole moment compared to NH$_3. \\$Conclusion:$\\$Among the given options, NH$_3$ has the maximum dipole moment due to its molecular geometry and the direction of the dipole moment.$\\$Therefore, the correct option is 3.