The most logical place to start is the Yellow 4 in the top-right corner. Given its position in the corner cell, it cannot be a 1x4 or 4x1 strip, as those would extend off the grid. Therefore, it must be a 2x2 square. This is our anchor point.

Placing the 2x2 Yellow square immediately defines the space for the Cyan 2. Its clue is on the far-right edge, and with the Yellow 4 above it, its only possible configuration is a 1x2 vertical piece directly underneath.

This sequence creates a contained 2x3 empty space in the bottom-right corner. Looking at our remaining pieces, only the Dark Green 6 can fit into this slot. This placement is a important step that unlocks the entire bottom row.

With the Dark Green 6 placed, the Red 6 is now forced into a 3x2 horizontal rectangle to its left. This action leaves a small 1x2 gap in the bottom-left corner, which is the only possible home for the Purple 2.

The puzzle now solves itself. The Light Green 2 must be a 2x1 vertical piece above the Purple 2. This carves out the top-left corner, forcing the Orange 6 into the remaining 2x3 space. The last large gap, a 2x4 vertical slot, is filled by the Blue 8.