The overview of the (American) Foxtrot basic forward step states a time of 4/4, and a counting of slow, slow, quick, quick.

(Forgive me if I'm using wrong terms. I'm new to ballroom dancing. But hopefully you get what I mean)

I can't find the 4th beat.

S S Q Q
1 2 3 a

I (think I) have been pausing/resting on the 4th beat, but my dance instructor keeps "correcting" me. Perhaps I'm misunderstanding something?

S S Q Q R
1 2 3 a 4

???

Foxtrot music is in 4/4 time, which means there are
four beats to a measure. A slow step takes two beats,
and a quick step takes one beat.

The American foxtrot basic forward step takes a total
of six beats, or a measure and a half:

S S Q Q
1 2 3 4 5 6 or
1 2 3 4 1 2

You have to do another pattern that takes an odd
multiple of two beats, such as another forward basic
step, to get back to starting on a 1 in the music.
Many of the bronze syllabus patterns in American
foxtrot take six beats, so you'll usually be starting
on a 1 every other pattern.

Once you start doing silver patterns, you'll have
more patterns that take an even multiple of two beats,
so it won't be so weird.

Don't worry about the half measures - well conceived groupings, and advanced dancers improvising will put together sequences that respect the musical phrasing. Also many of the more advanced figures are an integral number of measures - SQQ or SQQQQQQ etc. The six count basic exists to teach some movement skills, not because its wonderful musically.