Ok, let's take a take. There's 1 board, 3 PicoBucks, and 9 LEDs. Those purple connectors are called solderless terminals. They look like this:
[Image of Gardner Bender 4 Conductor PushGard™ Push-in Wire Connectors 10pk - Gardner Bender Part #: 25-PC4]
All of those holes are connected. So you plug in a wire from the input and then 3 wires for the outputs and you magically can split the wire into 3.
Here's the memorization part: on the above diagram, you will need to connect the 6 wires coming from the board (V+, V-, R, G, B, Gnd) to the 3 PicoBucks. So 6 wires requires 6 solderless terminals, for a total of 24 wires (1 input + 3 outputs = 4 wires * 6 terminals = 24 wires). 
Then each PicoBuck goes to 3 LEDs. Repeat the same procedure above. Connect the 6 PicoBuck terminals (R+, R-, G+, G-, B+, B-) to the 3 LEDs for a total of the same 24 wires. And there are three PicoBucks to do this to.
24 wires * 4 = 96 wires per lotus. I will be providing three different sizes of wires. There's a 5 meter long wire that connects the board to the connectors that go to the PicoBucks. Then there are 2' wires that connect those connectors to the three PicoBucks, so that they can sit a few feet away from each other and spread out among the petals. Then there are 6" wires the connect those PicoBucks to the individual LEDs, which should all go in slightly different directions.