The Red 9 in the top-left corner is the most starting point. The number 9 can only be formed by a 3x3 square. Since its clue is in the corner, its placement is absolute: it must occupy the entire 3x3 top-left section. This one move defines a massive portion of the grid's boundary.

Similarly, the Orange 4 in the bottom-left corner is a prime candidate for a 2x2 square. Placing it as a 2x2 in that corner establishes the bottom-left boundary. While a 1x4 is a possibility, the 2x2 is a much more common and stable configuration, and good practice is to test the most probable shapes first.

With the Red 9 (3x3) and Orange 4 (2x2) locked in, a 1x3 vertical slot is created between them. This single move connects the top and bottom halves of the puzzle.

The placement of the Red 9 leaves a 2-cell wide space to its right in the top row. The Gold 2 fits here as a 2x1 rectangle. This, in turn, leaves only a single column on the far right of the grid. The Teal 4 clue is in that column, forcing it to be a 1x4 tall rectangle.

The board is now falling into place. A large, 2-cell wide gap exists between the shapes on the left and the Teal 4 on the right. The Light Blue 6 must be a 2x3 rectangle to fill this space. The final remaining area in the bottom-right corner is a 3x2 space, which is a perfect home for the Dark Blue 6. The last piece, the Purple 2, fits neatly into the 2x1 slot left between the Red 9 and Orange 4.