The most logical starting point is the Purple 4 in the bottom-left. A region of area 4 can be a 1x4, 4x1, or 2x2 rectangle. Given its proximity to the grid's corner, both the 1x4 and 4x1 orientations are impossible as they would extend off the board. This forces it to be a 2x2 square, immediately defining the bottom-left corner of the puzzle.

With the 2x2 square in place, look at the Purple 3 clue directly above it. As 3 is a prime number, its region must be a 1x3 or 3x1 rectangle. The newly placed Purple 4 region forms a wall below it, making a 3x1 horizontal shape impossible. Therefore, it must be a 1x3 vertical strip.

Now, let's jump to the top of the grid. The Orange 2 clue must be a 1x2 or 2x1 rectangle. The Teal 3 clue sits directly in the cell below it, physically blocking a 2x1 vertical orientation. This forces the Orange 2 into a 1x2 horizontal shape.

These initial, certain placements create a cascade of solutions: The Teal 3 clue, now boxed in by the Orange 2 and the edge, is forced to become a 1x3 vertical strip.

The region for the top-left Dark Green solid is now confined by the grid edge and the new Teal 3 wall, leaving only a 2x3 rectangle as a possible fit.

This pattern continues across the grid. The Teal 6, for example, is now bounded on multiple sides, forcing its 2x3 shape. Each solved piece simplifies the next, leading to the final solution.