All Candidacies of # w/in Region Alligned =
Though likely written somewhere in this site already:
Two or three of the same candidate forming a line in a region eliminates that candidate as a possibility for the rest of the row/ column.
4 is eliminated in the bottom three cells of the left region by the four in the bottom row of the the right the right region.
The top row of the left region is full of things not four. Thus the only places left for the four are in the middle row of left region.
If a four were to be placed in any of those spaces it would eliminate four as a possibility for the middle row. The four can not exist anywhere else but that row in left region. Thus you can say with certainty:
If you can draw a single straight line through all candidacies of a number within a region (region size limits two-3), they can be eliminated from the rest of the row or column.
Commonly this is useful as it is in the example. This rule eliminates up to six spaces in a row/column. Here, with the bottom two rows eliminated from the middle region, there is only one space left for four. To the right of 6.
~ represents 4's candidacy
Here, with just two, aligned candidacies it still eliminates the middle row of the top regions.