20 kHz PWM frequency at 8 bit duty cycle resolution = 20,000×28 = 5,120,000 or 5.12 MHz clock.
20 kHz PWM frequency at 16 bit duty cycle resolution = 20,000×216 = 1,310,720,000 or 1.31 GHz clock.
Remember, during each PWM period, the your counter counts through all values.
The Nexperia 74HC393 and 74HCT393 maximum clock frequency depends on supply voltage, but at 5V you can expect at least 20 MHz (but in room temperature up to 99 MHz). 20.48 MHz clock can provide 10 bit duty cycle resoution for 20 kHz PWM; 81.92 MHz clock 12 bit.