(Let's start by assuming that you are using the common flamenco approach of starting the cycle of 12 beats on "12". This is highly confusing to most trained musicians, but it makes sense if you think of beginning the count on a clock face, which of course starts at the top, on 12).
Keep in mind that there are number of distinct regional styles of Soleares, the Grandmother of the Palos, and I'm just an infant wandering in the great cathedral of flamenco, so I won't try and explain those differences...
But a simple place to start is just to listen - here is Juan Habichuela (accompanying the incredible 20-year old Estrella Morente!) - he is famous in particular for his solid and responsive accompaniment of cante. His introduction is a small masterpiece of clarity, atmosphere and imagination:
While he will lead to a strong 3 with the classic three chord flamenco cadence ("1-2-3" -> G-F-Emaj), He will almost always drop a golpe on 6 and 12, helping the singer keep track of the compas, even when they are singing freely over the cycle of beats. Another "flag" he frequently sends up for the singer is the characteristic Soleares arpeggiation pattern on 10-11-12 that pushes to a strong 12 accent (with golpe).
You teacher is right about 6/8/10 as well - the accents on 6, 8 and 10 serve to divide up the second half of twelve beats into groups of two, a very characteristic flamenco shift in accents. So you could think of the twelve beats as "two-groups-of-three, followed by three-groups-of-two" - (>> > >) (>> > >) (>> >) (>> >) (>> >) - speed that up and you'll start to hear the rhythm of "I Want To Live In America" from "West Side Story"!
But just listening to this roomful of master musicians is an education in itself - Ole!