The Orange 9 is the perfect starting point. On a 6x6 grid, a rectangle with an area of 9 has only one possible dimension: 3x3. Any other configuration (1x9 or 9x1) is too large. The hint is located in the cell at column 2, row 1. To contain this hint, the 3x3 square must occupy columns 2-4 and rows 1-3. This single placement is the key that unlocks everything else.

With the Orange 9 placed, the Blue 3 (hint at C1, R2) is now pinned between the orange block and the left edge of the grid. The only way to form a 3-cell rectangle in this 1-cell-wide gap is a 1x3 vertical strip, filling C1, R1-3.

The top of the grid now reveals its structure. We have Blue, Orange, and two empty columns on the right (C5-6). The Green hint (for a shape of area 2) sits at C5, R1. A 2-area shape can only fit here as a 2x1 horizontal rectangle at C5-6, R1.

This leaves a perfect 2x2 hole at C5-6, R2-3. The Gold 4 hint is at C6, R3, which falls right inside this empty block. The Gold 4 must therefore be the 2x2 square that fills this space. The entire top half is now complete.

Moving to the bottom, the Purple 4 (hint at C1, R5) cannot be a 1x4 rectangle, as the space below the Blue 3 is only three cells tall. It is forced to expand sideways, becoming a 2x2 square at C1-2, R4-5.

This forces the Red 4 (hint at C2, R6) to be a 4x1 strip along the bottom at C1-4, R6. The remaining gaps are now defined: a 2x1 space for the Light Brown 2 at C5-6, R6, and a large 4x2 space for the Teal 8, which neatly fills the rest of the grid.