Here are four observations of the reactions of four metals
Before starting of with my reasoning , I must tell you that your answer ( whether guessed or logically reasoned ) looks correct according to me .

I am assuming that you are familiar with the Metal Reactivity Series ( if not look here )

We shall take use of a well presented reactivity series :

 

Now to crack the answer clue by clue :

1.


  Metal F and G react slowly with water.


Hence F and G are somewhere at the top.

2.


  Metal H displaces metal G from its chloride salt solution


Clearly H>G.

3.


  Metal E does not react with dilute acids 


E will come somewhere at the bottom half so F,G>E (from 1) and we can further say H>G>E (from 2)

4.


  Metal H does NOT displace metal F from its sulphate salt solution 


This gives F>H.

Combine last two clues' result to get F>H>G>E .