That look an interesting project.
By looking at the picture, and trying to understand of what you trying to do, it look like you are trying to do a VU meter by using leds.
I will try by using one led per output pins. Not 4 leds per output ... not yet. The principle work like the Knight Rider light bar. To simulate a music signal, a pot connect to an analog input will do. After that, you can try to code and test if it work or not, and re-code and re-try and re-code again and re-try until you got what you want.
The leds can be connect like --- > output pin -- resistor ( 220 to 470 ) --- anode - Led - cathode -- GND. Code ---> need an HIGH to light up.
To display 4 leds per output, you need an external voltage supply in order to power 4 leds - 4 leds in series will take about 8 V. 2 V per led @ 10 mA, control by a transistor. You can use the ULN2003 https://www.seeedstudio.com/document/pdf/ULN2003%20Datasheet.pdf and connect 4 leds in series with a 100 ohms resistor at the output of the ULN2003 like ---> output of the ULN2003 --- Led 1 --- Led 2 --- Led 3 ---Led 4 --- resistor 100 -- +9 V for a 12 V use 470 to limit the current around 10 mA. Connect the input of the ULN2003 at the output pin of the Arduino. Code ---> a HIGH will turn ON the Leds. The rest is just coding the Arduino to get the output / pathern you want when the music is playing.