How would you predict 4,4-difluoroglutamate would be metabolized?

Are you sure that's how the question is stated?

That should read cofactor, it's an important cofactor in DNA synthesis, and glutamate is replaced with I, I being 4,4-difluoroglutamate.

The chemical structures of both folate and folic acid consist of three ringed structures plus one or more molecules of the amino acid glutamate (or glutamic acid). The number of glutamate molecules affects the absorption and metabolism of folate or folic acid in the body. The folate food form has many glutamate molecules attached. Enzymes in the intestine have to remove these glutamate molecules until there is only one left, before folate can be absorbed into the bloodstream.

Now what you're saying in the question is that they created a folic acid analogue where instead of glutamate, they've attached 4,4-difluoroglutamate. So, once this analogue enters the cell, 4,4-difluoroglutamate can start getting metabolized. The thing is, often fluorinated amino acids cannot be metabolized in the same way as the usual ones can. I'm guessing the fluorines would get removed and the glutamate would get metabolized in its usual way. Not sure...