I'm a little confused, although i get the main idea. I use the Lose It! app and it calculates the grams of carbs, which I'm trying to keep aware of and around 100g a day as best I can.

Now say hypothetically a food item has 10g of carbs per serving. 6 of those grams are fiber, and 4 of them are sugar.

Do those 6 fiber grams count towards my total grams per day of carbs?

It depends on how the app calculates it and might be better to ask the app developer. I think it does but then again, I never noticed.