Example, Part 2
Now that you have crossed out some squares, you can fill in others. You can add some squares to the "4" row because of the Xs to the right. You can add one square in the "5" row. Also, you can use the overlapping technique in the "3" and "4" columns on the right side.
Now, in the "2" column, there is one square that must be part of the 2, so you can X out many squares in that column. In the "1,6" row, it is not clear whether the single filled square near the top is part of the "1" or the "6". If you fill in the two white squares between the black ones, you might be making a mistake; the single square may be the "1". The two black squares below it are clearly part of the "6", though, and you can fill in one more square below them; it will be filled in no matter what. The "6" column to the right needs another X near the top where the 6 can never reach. You can add more Xs in the "3,1" row, between the filled-in squares. The first row of "8" is complete, so just cross out the rest of the white squares. The second "8" row has a gap in it that must be filled in. That will complete the row, so the rest of the squares can be crossed out.
The top row now only has one way to fill in two squares, so those get filled in. You can cross out the single unfilled square in this row. The 4 row below that can get the final square filled in to complete that row. The 7 row below that can also be completed, with white squared crossed out. The 5 row can get two more squares filled in to the right of the ones that are already filled in. You can fill in one square in the middle of the five empty squares in the 3 row at the bottom.
The 1 column has been completed, so X out the empty squares. You now know where the 6 is in the 1,6 column, so fill in the remaining black squares and X out the empty ones. The 9 column is also completed, so X out the bottom square. The 6 column has been completed, so X out the top square that is empty. The second 5 column can be completed, so fill in the remaining black square and X out the empty one. The 4 column to the right can be completed; fill in the black square and X out the empty one. In the 3 column to the right, X out the last empty square. Then, in the 4 column at the right, fill in the last black square.