Differences in boiling points between molecules are due to varying strength of intermolecular forces. From the data given, we know Br2 must have the strongest intermolecular forces as it has the highest boiling point, followed by NH3 and then F2. We can then use our knowledge of these molecules to determine the intermolecular forces present.
NH3 has hydrogen bonding as the intermolecular forces, as this is only present between H atoms and highly electronegative atoms such as N. Both Br2 and F2 consist of 2 equally electronegative molecules, so Van der Waals' (VdW) forces are the intermolecular forces present. From the order of boiling points, we can determine that the VdW forces in Br2 must be stronger than the VdW forces in F2 - this is because Br2 has more electrons which can create temporary dipoles. The hydrogen bonding in NH3 is stronger than the VdW forces in F2 but weaker than the VdW forces in Br2, leading to the differences in boiling points seen.