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Attached is an example of a 2-column proof. Note that a diagram is shown at the top. Note that the Given (hypothesis) is shown at the top. Note that the To Prove (conclusion) is shown at the top. The proof follows.
Your problem has no "Given" and no "To Prove." So, we do not know where we are beginning nor where we want to end. The list of possible reasons and definitions is handy but is of no use without a specific Given and a specific To Prove. Without that information, I can't help.
I agree with @Directrix there is no given information. It seems like the first part of this problem was cut off?
my guess is that it should say something like Given: HG || IF, JH = JF again this is a total guess (but it's a guess based off previous experience with similar proof tables)
is it possible to show the entire worksheet?
maybe the given info is buried somewhere in another problem
then you'll have to ask your teacher to provide the "given" data. Only s/he would know that
the reason "alternate interior angle theorem" does imply that HG || IF will come into play somehow
so that's why I assumed `HG || IF` was one of the givens