First, get yourself a ULN2803. Connect one output each to the common cathodes. Connect the Common to the Arduino Gnd.
The Arduino will connect to the anodes via current limit resistors.
The Arduino will connect to the ULN2803 inputs.
You drive a pattern for column 1 on the anodes, and drive common cathode 1 on for 2ms.
You drive a pattern for column 2 on the anodes, and drive common cathode 2 on for 2ms.
Repeat for columns 3-4-5-6-7-8.
That is multiplexing. The eye/brain is tricked into thinking all 8 columns are on together.