Hi,
I need help with the following question :
What is the relative nucleophilicity of the following in a polar, protic solvent:

Nucleophilicity requires that we look a the availability of the electrons.  Here, 2 systems are with O atoms,  i it is negative making the electrons more available.  In iii we have a N system in ammonia. Since N is less electronegative than O, the N system is a better electron donor and so a better nucleophile ie. ammonia > water.
so i > iii > ii