DNA testing, need practical advice.

Which of those have done any testing at FamilyTreeDNA?

FamilyTreeDNA (FTDNA) currently has a Sale thru Aug. 31 -- if your father has not already done the FamilyFinder Test at FTDNA, and has not done any DNA Testing there - then buy the FamilyFinder Test for him, and the highest level Y-DNA Test you can afford at this time -- at the same time, for the same Kit, before Sale ends.

your father ->your g'father -> your g'gfather ->yr 2nd g'gfather -> your 3rd g'gfather ->yr 4th g'gfather -> yr 5th g'gfather -> your 6th g'gfather
-- I do not understand -- you say he is a 5th generation descendant of your 6th great-grandfather -- to me, seems your father is 7th generation descendant of your 6th great-grandfather
Cannot provide further advice until I understand how you are using the terms / where the misunderstanding is - but definitely, if you can at all afford it, get at least the FamilyFinder and YDNA37 [at very minimum] for him, if you do not already have that, higher level YDNA if you can afford it.

Nobody has done any testing yet, we want to do the testing that will give us the answer as to whether these two men were brothers.
And you are right, I did not count the generations right. We are talking about my 4th great grandfather and my fathers's 3rd. To be more specific- my father (Andy), his father (Samuel) his father (Paul) his father (Ezechiel) and his father (Samson). I am trying to determine if Samson was a brother to Herman. The descendent of Herman I am in contact with is the same distance from Herman as my father is from Samson.

-- what I see is
you -> father (Andy) -> g'father (Samuel) -> great-g'father (Paul)
-> 2nd g'g'father (Ezechiel) -> 3rd g'g'father (Samson)
and then to Samson's Father = your 4th GreatGrandfather

Do I have that right?
And you are thinking Samson and Herman are a sibling pair,
it is 4 generations up from your father to Samson, and
4 generations up from the descendant of Herman to Herman --
so those two, if you are correct, are 4th Cousins.

At least 90% of the time, if folks are 3rd Cousins, FamilyFinder will find them as a Match. For 4th Cousins, it is at least 50% of the time. For 5th Cousins, it is at least 10% of the time. For 6th cousins and beyond, they say it is typically less than 2%.

At the 4th Cousin level, it is sort of iffy, but you could get lucky and get very helpful results with FamilyFinder.

Testing as many as possible will definitely be helpful.
One of the wonderful things FamilyTreeDNA offers for the FamilyFinder Test is the Chromosome Browser, where you can compare up to 7 Profiles at once.
If your father plus his suspected 4thCousin1 and his suspected 4thCousin2 all match in the same place on Chromosome Browser, that is an indication that segment comes from a common Ancestor. I have seen people claiming very small segments are meaningful to them, and the experts saying one cannot have confidence in their being meaningful unless they are at least NNN cM long.

If everybody is willing to test, and you have thousands of dollars to easily spend now, then order FamilyFinder and YDNA-700 for each of them while it is on sale now. Otherwise, you will have to choose. Definitely for your father, order the FamilyFinder Test.

From various places on FTDNA,
1] "Most Y-DNA67 exact matches are related within six generations. That is 4th cousins. Family Finder test will detect a relationship between only about half of all 4th cousins." -- Note it says "Most" - it does not say "all"

2] If folks match on Y-DNA, then they have a common ancestor along the Paternal Line - A 0-step match -- ie, an exact match -- on any of Y-DNA37, Y-DNA67, YDNA111 - each "suggests the common ancestor is within the time frame that surnames were adopted in Western Europe."

FamilyFinder gives you an idea how closely related two folks might be -- but not along which line. Since 4th Cousins are only found as matches about half the time, not being found as a match does not mean not a match.

Y-DNA lets you know if two folks are related along the straight paternal line -- but if you tested at the lower levels, it could be many, many generations back to the common ancestor. Mutations creep in, so not an exact match def. does not mean not a common ancestor - but there is no way to know for sure how many mutations at what level of testing mean exactly how many generations back to the common ancestor.

Unfortunately we do not have thousands to spend. For now we ordered the Y DNA37 for my father and the suspected 4th cousin. I was hoping for better odds. Now I am hoping we get lucky.
Thanks for the input.

That is a reasonable choice. Hope you will let us know what it shows about the two of them - if they match, and if so, at how many steps.

If at YDNA37, they are not a match and not even in the same basic Haplogroup, then you have disproved your hypothesis - they are not the direct male descendants of brothers.

If they are not a match, but are in the same basic Haplogroup, you may want to consult with the Administrator for that Haplogoup's DNA Project to see if there is any possibility / what you might perhaps check -- since it is possible they miss by just a tad beyond the cut-off for Y-DNA37, might possibly match at Y-DNA67 -- or might be they miss by lots.

If they match, but not at 0-steps, again, may be worth checking with the Administrator of that Haplogroup's DNA Project for how meaningful that is. Possibly check, even if 0-steps.

Out of curiosity, did you send it to the descendant in Israel or the one in Hungary? And is the other one also willing to test?