Short and "to the point" answer: Those numbers are just identifiers for various school district organization plans. The digits refer to the number of years a student spends in each "section" of a schooling system.
The general notation is A-B-C, where "A" is the number of years in primary school (elementary school), "B" is the number of years spent in middle/junior high school, and "C" is the number of years spent in secondary (high) school. 6-3-3 and 5-3-4 were both fairly common at the time, but recent (proposed) policy changes in the Brooklyn school systems led to confusion and even outrage in the area. More details on the specific meanings of the numbers are included below.
That sign is simply mocking the changes, as a "2-2-2" system doesn't exist (and is in fact completely nonsensical) and "?-?-?" is seemingly a way of asking "What's next? How much longer are we going to mess with the system, treating our children like pawns in some game of political chess?". The numbers almost certainly aren't referring to dates or court cases.
Detailed answer (the most important details are bolded):
It's important to note that this is the source of the image. The photo was taken on April 14, 1965 and submitted to the Associated Press image library in 2011. The submission notes for the photo read as follows:
"Pickets from the Parents and Taxpayers Association march outside the city Board of Education building in Brooklyn, New York, April 14, 1965. The demonstration was held to protest a report submitted to the board by school superintendent Calvin E. Gross. The report was called a "blueprint for further action toward quality integrated education." Two groups picketed the building opposing the report, the other was headed by the Congress of Racial Equality."
If we're hoping to learn more about the specific protest featured in that photo, then this description tells us some pretty useful information. Apparently this crowd was protesting against the ideas of a man called Calvin E. Gross. Gross, according to his obituary featured in the New York Times, was the superintendent of schools in New York city around the time that this photo was taken (particularly, in early 1965). Apparently, he was asked to resign after a storm of criticisms and controveries due to the report he released, referenced in the blockquote.
I'm not entirely clear on what exactly this report was, but we can learn a lot about what Calvin Gross was proposing from other information at the time. According to yet another NY Times archive I found, this time dating to mid-late 1964, Gross was fairly vocal about his plans for the integration of segregated schools. On top of unspecified "proposed steps", he also intended to immediately pair up "four sets of elementary schools", create five additional "Educational Complexes", and change up the year sequence of the school districts, namely adding one year to high school (presumably so that the year systems of various segregated schools matched up, in order to ensure a smooth integration). Gross was planning to spend around $4.3 million on all of this. As you can imagine, the vagueness of some of these announcements (as well as the cost) naturally irritated many people who would be affected by the changes.
Let's set that aside for a moment and go back to those numbers themselves. Since the image description describes the protest in relation to education troubles, the meaning of the numbers in this case must be whatever relates them to the education system. This paper reveals what the numbering system means, and details the history of their relevance to school programs in the United States.
Personally, I went to school in a 4-5-3 plan, but it seems that the 5-3-4 plan is most common nowadays in the United States. Notice that the sum of the three numbers is always 12, since it represents the twelve years of primary through secondary school that students take.
Pre-1960's schools systems often didn't even have middle school or junior high, leading to more of an "A-C" system. Sometimes the notation is extended to include A-B-C-D, where "D" refers to the number of years typically spent in college or university for a particular area (i.e. 4). The notation can be extended even further as X-A-B-C, where "X" refers to Kindergarten, preschool, or whatever it is chosen to represent in a particular instance.
Despite these special cases, the more general A-B-C notation is most commonly used (...not that any of this knowledge is "common" to begin with. I had to do some serious sleuthing to learn all of this, and now my entire afternoon is gone!). It's also worth noting that there is no such thing as a "2-2-2" system. Those numbers don't even add up to 12!
Anyways, the 6-3-3 system of learning (6 years of primary school, 3 years of middle school, 3 years of high school) was starting to become pretty common in the New York City area during the 1960's (I live in New York and it's actually still not uncommon), but it wasn't exactly something people were used to. So when Calvin E. Gross suggested adding a new year to high school, implying a sudden shift to the 5-3-4 plan that was just starting at the time, I imagine that annoyed quite a few people!
One of the common criticisms of Calvin Gross' proposed system that I described above comes down to the fact that he was proposing a lot of sudden changes to the education system that many were uneasy about, something that always gives rise to outrage from the public.
It's pretty clear from the photo that this is what the protest was about. The "DON'T MAKE PAWNS OF OUR CHILDREN" and "HASTY IMPLEMENTATION" signs make it obvious that the people are protesting sudden and uncomfortable changes, which is consistent with all of the evidence described above.
I believe the sign on the left was trying to emphasize the supposed ridiculousness of the changes that were supposed to have taken place. In a "We recently had to adapt to the 6-3-3 system, and now we might already need to switch to the 5-3-4 system all in the name of racial integration???" sort of way. The "2-2-2" part of the sign was just mocking the numbering notation entirely in a "What are we going to switch to next?" manner, and the "?-?-?" part is clearly a continuation of the point: "What comes next? Where does it stop?"
I completely disagree with the comments saying that the numbers refer to dates or Supreme Court decisions. X-Y-Z is an extremely unusual notation for representing dates, and one that I've never seen before, not even in the early 1900's. That interpretation also doesn't add up with all of the evidence and points I've presented that are directly supported by the original description of the image.