How to solve this 6×6 logic puzzle

6×6 · severe · 22 steps

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This 6×6 board rates as severe (difficulty score 1248). Solving it from scratch takes 27 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

First, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
Next, every remaining candidate in this region touches E5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, marking D1 would immediately leave region 2 with no open cell for its marker, so it can't be the marker there.
After that, every remaining candidate in this region touches B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Now, every remaining candidate in this region touches A4 and C4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
From there, if E1 were the marker, it would force F3 (the last open cell in region 4), then D6 (the last open cell in region 6), then A5 (the last open cell in region 5), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
Following that, that one can't be the marker: at F1 it would force D6 (the last open cell in region 6), then A5 (the last open cell in region 5), then B3 (the last open cell in region 3), and row 2 would be left with no open cell for its marker.
First, every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
Next, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, marking E2 would immediately leave region 4 with no open cell for its marker, so it can't be the marker there.
After that, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
Now, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
From there, that one can't be the marker: at C1 it would force D3 (the last open cell in region 2), then B4 (the last open cell in region 3), then F2 (the last open cell in region 4), and row 5 would be left with no open cell for its marker.
Following that, place a marker at A1. Region has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
First, if F2 were the marker, it would force D3 (the last open cell in region 2), then B4 (the last open cell in region 3), and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
Next, place a marker at D2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
Then, together, two regions have open cells only in rows 3 and 4; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
After that, marking F3 would force B4 (the last open cell in region 3), and then row 5 would be left with no open cell for its marker. So F3 can't be the marker there.
Now, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 1 touching neighbour.
From there, place a marker at B3. Region has exactly one open cell left.
Following that, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region.
Finally, place a marker at C5. Region has exactly one open cell left.

The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎