The hexagons on the left give an ordering.
Oddly, 180-DEGREE turns are more straightforward here. For the other cases, you'll find position trumps value.
Don't be a DUMDUM with the DEGREEs (and we don't mean the JD kind).
There's only one way to write 2 and 6, but there are two ways to write 1, 3 and 5, and four ways to write 4. Conveniently, you can go all the way up to 26.
Once you have any group of six gears, you'll want to replicate a familiar pattern.
For any gear, rotating in one direction will turn a ternary-encoded word from the left column to one from the right, possibly offset.
Rotating the same amount in the other direction will position the new word's letters so that they start from the top... and more importantly, will turn a set of gears' centres from one word to another.
In the six sets of correct six-gear sets, you should see the words JAMMED, MONDAY, RIGOUR, UNLINK, AMOEBA, and FLAPPY.
In this last iterative step, the derived six middle letters won't anagram to give a new word, so use the ordering already given and only take the transformed letters to get your answer.