This may be incorrect (it was gleamed from a pretty old video: https://www.youtube.com/watch?v=7tYxK8DZKYU). So if anyone from Numenta see’s this and notices something wrong, please don’t hesitate to correct me. My intention isn’t to misrepresent you.
That said, to my understanding, Layer 6a and 6b are the layers that perform the columns actual spatial-coordinate processing. L6a measures orientation via modified HD cells, L6b measures location via grid-like cells. They then communicate their findings via the depolarization of neuronal mini-columns found in Layers 4 and 5b.
(PS: The way it was described in the video made it sound as though layers 2 and 3 essentially worked together to perform the same functions as layer 5a. So in my descriptions I describe them in combination, simply as “layers ⅔”…)
Layers ⅔ and 5a serve as the output layers for the column. These layers are capable of temporal pooling; that is, remembering input stimuli over a given time-length. These layers, working with with layers 4 and 5b, comprise much of the columns predictive processing function.
We can view each column as essentially being comprised of two sensory motor subsystems. As you could likely tell from earlier, one of those subsystem is processing location. The other is processing spatial orientation. Layer 5b is serving as the input for that second subsystem. If we were to blow the diagram apart into these corresponding subsystems, it might look like this:
Also, it might help if you’re able to wrap your head around the processing of information as it progresses through the columnar structure.
To my understanding, the data flow would look like this:
New input enters the column through Layer 4. Layer 4 is part of the spatial orientation subsystem (as highlighted by the blue coloring). Its responsibility is twofold: to track incoming object orientation, and to make predictions about that object’s future orientation and scale. It does this via the following:
(1) New data enters layer 4. At time of input, the subsystem does not yet know the orientation of the token represented by that input. However, based on previously learned experience, Layer 4 may attempt to make a prediction as to what that orientation is, polarizing a number of its intra-columnar neuronal populations in the process…
**Fun fact: Layers 4 and 5b are each capable of sequencing patterns. They are the layers responsible for the column’s ability to build models and remember the world. As such, each layer contains approximately 5000 neurons and during any given sparse activation (a reaction to a given input) 100 of these neurons will become active. This method of sparse activation gives each layer 3X10^211 possible neuronal sequencing patterns within its search space–each of these patterns representing a unique token. Additionally, the average pattern overlap is ~2%, making them tolerant to noise and fault.
…As it does this, Layer 4 will bifurcate its throughput off into two directions:
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It will send a projection up to layer ⅔.
Layer ⅔ is a temporal pooling layer and, as such, is stable over time. This projection is essentially Layer 4 saying “I predict the input to be the following…” Layer ⅔ will then open its search space for all available models matching the Layer 4 prediction. As additional input is projected into L⅔ from L4 that search space will narrow until only a single representation remains. They have a pretty good write-up on it here: Frontiers | A Theory of How Columns in the Neocortex Enable Learning the Structure of the World
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Simultaneously, Layer 4 will send a second stream of information down to layer 6a. Layer 6a will then process the input through the use of modified Head Direction (HD) Cells. Once L6a processes the true orientation of the input signal it will depolarize a range of neuronal columns found within L4. (I’m a little unsure as to how layer 6 is processing the information tbh. My intuition says to look into how the hippocampal complex does it, and possibly the cerebellum. But I’m not 100% sure. Need to look more into this myself…)
These ‘neuronal columns’ are often called ‘minicolumns’ and are a critical component in a column’s ability to perform predictive processing. We’ll find these minicolumns all throughout the broader columnar structure, but they’re especially prevalent in layers 4 and 5b.
(2) With the minicolumns in L4 depolarized, L4 will then relay the correct orientation back up to L⅔. If L4’s initial prediction proved correct everything will continue as normal.
(3) L⅔ will now take its information and send it off to Layer 5b. In this way, the output of one subsystem becomes the input for the second.
(4)This entire process will now repeat for the second subsystem. However, instead of measuring orientation it will now measure spatial location via grid cells. When the second subsystem has finished, Layer 5a will release a motor-behavioral output, affecting bodily functions, movements, and/or other cortical processes. (What it affects depends on the positioning of the column itself.)
Hopefully this is somewhat useful to you. And again, if anything is blatantly wrong with this, please point it out to me. I too would like my notes to be correct 
