The shuffle trick is a combination of two moves which is essential for self-multiplication.
The initial configuration is a FO node connected to two FOE nodes. The out ports of the FOE nodes are represented by big circles.
Each FOE node has the out ports coloured with purple and blue. After the shuffle trick there will be a configuration made by a FOE node at the root, connected to two FO nodes, such that each FO node has the out ports of the same colour.
This is done by a combination of FO-FOE and FI-FOE moves, which eventually shuffle two of the 4 out ports.