How to setup a 16x16 led ( 4x - 8x8 Leds) with 4 shift registers?
Think of the 16x16 array as one whole, not four 8x8 arrays.  One obvious way to multiplex the LEDs is with 16 rows and 16 columns.  If you have 8-bit shift registers, then you need two to control the 16 column lines and two more to control the 16 row lines.