You have
int latch=9; //74HC595 pin 9 STCP
int clock=10; //74HC595 pin 10 SHCP
int data=8; //74HC595 pin 8 DS
Pin 10 on the 595 is the reset pin and needs to be held high to allow the 595 to operate, The Clock pin should be connected to pin 11 of the 595.
Pin 13 is OE and need to be low for the outputs to work
Pin 14 on the 595 is Data in and Pin 12 is Latch
Like this ;
int latch=9; //74HC595 pin 12 STCP
int clock=10; //74HC595 pin 11 SHCP
int data=8; //74HC595 pin 14 DS
The diagram looks to have these setup correctly but wanted to mention it, You are missing 5V on pin 10 to enable the 595 so this may also factor in to why its not working, So I would check this first and see.
With all 4 cathodes tied to ground you will get all four 7 segment displays showing the same thing ; as I understand that's your current intended goal so that should be fine.
Also to note, the 4 digit 7 segment is multiplexed ; You cannot just connect all 4 cathodes ( assuming common cathode ) to ground if you want to display different things on each 7 segment as the ABC ect segments are common to each other so trying to display something on one 7 segment will show on the other three displays.
With the multiplexed 7 segments you need to switch each cathode to ground one after the other displaying the numbers one after the other ; do this very fast and they all look to be on.