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If both FeX2 & FeY3 are found to exist, X & Y can be : 

 (1) X = F, Cl, Br, I    ::   Y = F, Cl, Br 
 (2) X = Cl, Br, I       ::  Y = F, Cl, Br, I
 (3) X = F, Cl, Br      :: Y = Cl, Br, I
 (4) X = F, Cl, Br, I   :: Y = F, Cl, Br, I

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(1) X = F, Cl, Br, I :: Y = F, Cl, Br  is the correct option 


Explaination::

FeI3 does not exist as I reduces Fe3+ to Fe2+. 2Fe3+ + 2I – → 2Fe2+ + I2.

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