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Initial layout
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Movement paths
You will first need to move the bottom crate into the alcove on the right (as marked by the green line.) Once the crate is out of the way, you will need to adjust other crates in the counter-clockwise path. In the first cluster of three (marked by yellow lines), Move the bottom-left crate up one cell, the bottom right left by two, and move the first crate two cells below the top-right crate.
Next, handle the two crates at the north-east room. Push the crate in the alcove down by 4 tiles, and put the nearby crate in its place (or just at the entrance of the corner room).
Next, make room for moving the center crates. Move the top-right crate in the center one cell up (plus one cell right if you prefer getting a better path for visual purposes), and move the bottom-right crate up one cell. The final crate with the blue line is moved two cells right.
Once the crates are moved, you should have no difficulty getting all other crates into the target zone. When packing the crates, put the first three crates in the bottom-right corner, and the fourth at the top-left.