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Make a cartogram! The area of each rectangle is fixed. Find the right shape (aspect ratio) for each rectangle and fit them together. The layout on the left shows you the correct adjacencies (that is, which rectangles should be neighboring and how).
Use your mouse to change the shape of a rectangle.
Move two rectangles close to snap them together. If two rectangles form a bigger rectangle in the layout, then matching their common edge automatically groups them into one rectangle. Watch out for the red alignment indicators (cross and T-shape): if your rectangles are not properly aligned, then they cannot be merged.
Build the cartogram by iteratively grouping adjacent rectangles to form a larger rectangle.
The larger maps cannot be solved only by iteratively merging two rectangles. (Technically speaking, these maps are not sliceable.) You sometimes have to simultaneously merge groups of 5 or more maximal rectangles. (A maximal rectangle is a group of rectangles that together form a larger rectangle).
You have to build such maps in another way, namely using L-shapes.
All layouts in this game are L-shape destructible. That means that all high degree merges can be solved by iteratively adding rectangles to an L-shape.
If two rectangles form an L-shape in the layout then matching a common edge and a vertex lets you group them into an L-shape. Once the rectangles are properly aligned you can click on the red cross on their common edge and the game will group them into an L-shape. A number appears inside the L-shape that tells you how many maximal rectangles are grouped within it. You can use the mouse to change the shape of an L-shape.
You can add rectangles to an existing L-shape by matching a common edge and clicking on the red cross.
It's not possible to merge two entire L-shapes together. Therefore if you make L-shapes in the wrong order you can get stuck. In that case, you can break the L-shape apart again with a double click, and try another L-shape grouping. For the larger maps, the key to a fast solution is figuring out the best L-shape grouping.