Hm... don't rush up too much. One thing at a time.
What does double mean?
Double means 2, hence in the rate equation, you get:
x here is equal to 2.
The order of the reaction with respect to S2O8^2- is 2, not 0.05 or 0.5.
Now, post what you get for the second part, that is how the doubling of the concentration of iodide ions affect the rate of the reaction.
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Factor here refers to the number of times. Not a catalyst, or a condition for the reaction to occur.
I'm surprised you are doing this question without knowing this... :(