Connect Multiple L293D Motor Controllers to Arduino
The suggestion of using an Adafruit Motor Shield V2 for Arduino seems fairly good, although that particular shield controls only four DC motors at once.  That shield has a dedicated PWM driver chip on it, which removes the overhead of motor and speed control from the MCU.  That might allow you to drive four motors via the shield, and two via wires from the Arduino; or, stack two motor shields on the Uno.

If you definitely want to drive six motors from the Arduino, you may need to add a couple of control chips.  You could add a 74HCT04 hex inverter and a 74LS595, to create inverted drive signals and enable signals.  For example, the first PWM drive would go to L293 pin 1A and to '04 pin 1A; the first '04 output, 1Y, would drive L293 pin 2A.  One of the '595 outputs would go to L293 pin 1,2EN.

Alternately, you could use two '595s, with outputs to control L293 pins 2A; 4A; 1,2EN; and 3,4EN on each of three L293's.  The six PWM outputs from the Uno would go to 1A and 3A on the several L293's.  Using motor shields probably is a better idea, however.