To find out if the given reaction is a redox reaction or not we use oxidation number rules to find the oxidation numbers for each element in the reaction
+1-2 0 +1-2+1 +1-1
H2O + F2 ===> HOF + HF
as per the rules :
The oxidation number for an atom in its elemental form is always zero ==> F2 has a oxidation number of 0
In most hydrogen containing compounds, oxidation number of hydrogen is + 1.===> so H in H2O, HOF and HF is +1
Oxygen is usually assigned an oxidation number of -2 for oxides ===> so O in H2O and HOF is -2
Oxidation state of F in HOF is an exceptional case where F shows +1 oxidation state , which is proved by the fact that HOF is a strong oxidising agent which can not be explained if F = -1, H= +1 and O is given 0 oxidation state.
Therefore the oxidation number of F changes from 0 in F2 to +1 in case of HOF (since increase in oxidation number is oxidation we can say that F undergoes oxidation )
Also the oxidation number of F changes from 0 in F2 to -1 in case of HF (since decrease in oxidation number is reduction we can say that F undergoes reduction )
This is a reaction in which F undergoes both oxidation and reduction , hence its a redox reaction .