I’ve gone through the datasheet and one thing I’ve noticed is that ULN2803 has 8 input and 8 output pins, and 74164 is a 8 bit serial to parallel convertor. So I thing you are trying to make a 8*8 led matrix display.
Connect 8 output pins of the controller to 8 inputs of ULN2803. Connect your serial data_out pin of the controller to any of the two inputs of 74164, while keeping the other input pin high. Connect the 8 raws to the 8 output of 74164, and 8 columns to 8 outputs of ULN2803. And you scan the matrix column wise.
Cosider the first column,
Send 8 bits of the data to the input of 74164, Turn on the output of ULN2803 corresponding to the first column by making the respective pin of the controller high. Before going for the next column, turn of the current column. Do the same for all the columns.
You have so many sites