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Only six words put F first and F third, and five of them use the same vowel in between.
I takes the second box in five of the six, eighty three percent, and U takes the last one. So the page is the FIF stem plus a single outlier.
They share four letters and differ only at the end, and both are everyday words. If the last box is open neither is a good guess, because one leaves the other completely live.
Every word here uses F twice by definition, but the two Fs never touch except in FUFFY, which puts a third F in the fourth box. That makes FUFFY the one entry on the page that counts as a repeat.
E fills the fourth box in three of the six and T takes two. Those two cover everything except FUFFY.
So in practice the page is a choice between the FIFE stem and the FIFT stem, and then the last letter. Y closes two words and nothing else takes more than one.
Both are very common and they differ only in the last box. Whichever letter your puzzle confirms there settles it at once.
Someone who plays the fife. It sits with FIFED and FIFES on the same stem, all three separated by a single letter.
An F in the third box after another F is rare in English. The FIF stem does almost all the work and nothing else survives.