The description of first trick, and the solution of example puzzle has already posted.

Now let's see the second trick, and a new practise puzzle.

*If there are a 2 and 3 clue next to each other there is no rectangle that can part of both rows.*

*Similarly if there are a 3 and 4 clue next to each other there is no rectangle that can part of both rows.*

Because of every rectangle is at least 2 units wide. If a clue is 2 then there is only one 2-wide rectangle in that row. Similarly if a clue is 3 then there is only one rectangle in the corresponding row.

So a 2-wide and a 3-wide rectangle cannot be same.

Similarly a 4 clue can be a simple 4 or 2+2. It cannot part a 3-wide rectangle.

First I check if there is anywhere these kind of clues and I draw a bolded line between the two rows. It is a wall. These walls divide the grid into subregions.

In the next practise puzzle it is needed to use this trick and the previous one, too.

The biggest number is 9 in a 12x12 grid. There are 3 empty squares in that row, which seems too many.

But for instance there is a wall between R3 and R4.And it means that R3C7 or R4C7 is empty or both of them. These walls make it possible for the puzzlemaker to use a bit smaller numbers for starting.

Next time I will show the solving steps of this puzzle.