The Foxtrot basic takes 6 beats of music. The slow is 1,2 the second slow is 3,4 and the quick,quick is 5,6

I have to agree with KC and disagree with Don on this one.
You can't count a foxtrot reverse turn Slow - And- Quick-Quick as this is 4 steps and the reverse turn only has three.
I think we're talking about the same thing but in different ways.
The slow can be 1- and -a -half beats, and the following quick another 1 - and -a -half. This is a matter of an individual dancer's interpretation (that's how i dance it in fact, but there are other interpretations). This is one of the factors which make the foxtrot such an enjoyable and satisfying dance (when danced well, of course!)
I'm VERY uncomfortable with the idea of a slow being called slow-and. Why is there a problem taking 2 beats (or 11/2) on a slow, and still calling it a slow?

Is it worth pointing out that Ballroom Dancing in all its forms is an Art and not a Science. If you talk about spilt beat values how would one explain a Volta which is 3/4 1/4 . Or a Botofogo which is 3/4. 1/4. 1.I have two tapes on the Modern Waltz where in both tapes they split 3 beats in the first three of a natural and any other part of that dancee into 6 half beats. Both count out loud, 1 and 2 and 3 and.( lowering on the last and). If your wondering on what beat the feet close , it's on an and. Both of these gentlmen are top coaches in the UK, it would be hard to contradict either.

If you're talking about basic foxtrot as in dancing a basic quickstep, but more slowly (what we call "rhythm dancing in UK"), then Kevin is absolutely correct, and it works very well for social dancing.
If you try some more advanced foxtrot figures, such as feather step - reverse turn - feather finish, you will find the timing is Slow - Quick - Quick, with the slow occupying beats 1 and 2 and the two quicks each occupying 1 beat (making 3 and 4).
However, the beauty of foxtrot is that it can be very sophisticated in its rhythms, allowing the dancer some leeway to use his own musical interpretation, departing from the strict 2 beat slow and 1 beat quick structure. All this pleasure is ahead of you!!

I think that foxtrot is the dance that most
epitomizes ballroom dancing. It is a dance of
structure and elegance, and if not appreciated
as such, should probably be left alone.
American style is not very standardized and
is probably not taught the same in any two places. But, the basic step is usually
S S Q Q or S Q Q. English style actually has no
core basic, but is progressed around the floor
through various figure combinations that are
comprised of slows and quicks.