How to read datasheets effectively to connect components safely?
Then how will I go about answering this question systematically

That's something that you may need to understand the datasheets for – but mainly, you simply need to know basic electronics, to know what of the datasheets is relevant to you.
So, the systematical approach would be called &quot;circuit design&quot;, I'd say.
In the relatively straightforward case here:
The LEDs pose a load to a driver, your AFE. You need to figure out how large the load that your driver can operate is.
Now, &quot;How large can the load be&quot; is about as multi-faceted as &quot;how much can you carry?&quot;: You'll need to say under which performance requirements: If you still need to be able to run, that will be less than if brisk walking is fast enough. A load of 50 kg of apples is easier to carry than a load of 50 kg of angry bobcats thrashing around in your backpack.
Same applies here: I haven't even looked into the AFE's data sheet, but there's going to be tables and graphs that tell you how much current and voltage your driver can supply; with how much capacitive loading it can work; how the load needs to look like for maximum power; maybe something indicating how much distortion you get for a specific output power.
You need to first figure out what your application needs (e.g. how much distortion can you tolerate? Which bandwidth do you need at least?), then you can look up how much load your AFE can drive and still achieve that, then you can figure from your load's datasheet what that means with respect to the number of LEDs.

TL;DR: the shortest path from 0 to result is &quot;engineering&quot;, so engineer.