Need help: How to make my own 24x16 LED Matrix display

You can wire all the rows together (making an 8x48 matrix) and use a single shift register to drive the rows. That means 7 more for the columns or 8 shift registers total. SPI can output at about 8 megabit per second so you can update the registers about 143,000 times per second. That means all 8 rows at almost 18 kHz.