which of the compounds has the strongest hydrogen bonding
You can compare the strength of the hydrogen bonding by comparing the electronegativities of the other elements. All the four elements, Br, F, Cl and I belong to the same group in the periodic table: group 17 named halogens. Then the kind of bonding they form is similar: polar covalent. You must know the trend of the electronegativities in the periodic table. Electronegativity decrease when you down across a group. Then the electronegativity of F is the higher of the group (indeed, it is the highest of all the 118 elements) . The higher the electronegativity the stronger the attraction that the halogen attracts the electrons and the stronger the hydorgen bonding. Then, the conclusion is that HF has the strongest hydrogen bonding.