I am not sure I understand your problem. I can't quite tell what the wires are connected to from the photographs, and there are lots of corrections on the other site.
If you explain what you are trying to do, folks may be able to give better advice.
Have you got a L293D datasheet? There are several block diagrams which explain things, but you need to be careful to use a diagram which fits what you want to do. If you explain which datasheet you have (the URL), and what you are trying to do, I could probably identify the appropriate diagram
Let me try to explain how to connect the chip. (I assume you understand how the pins are identified, and that the colour of the wires makes no difference:-)
The chip is in two largely independent halves. Lets call them A and B.
Half A: Pins 1, 2 and 7 are the inputs, and pin 3 and 6 output to motor A.
Half B: Pins 9, 10 and 15 are the inputs, and pins 11 and 14 output to motor B.
The enable pins (1 and 9) switch the outputs to the motor on (low resistance, and hence connecting it to power or ground) or off (very high resistance, so a motor would eventually come to a stop as no current flows).
There are several different ways of controlling the motor.
Here is one way, but there are, at least, two others.
In this approach, the PWM signal is connected to the Enable pins. This allows the PWM signal to provide speed control.
You will connect 3 Arduino pins to 3 input pins on each half of the L293D.
Connect an Arduino PWM pin to pin 1 (half A), and another PWM pin to 9 (half B).
You will use analogWrite for those two PWM pins to control the speed.
The other two Arduino pins for each side control motor direction.
Set them up with pinMode in setup. then ensure they are DIFFERENT, e.g. if pin 10 and 11 are used do:
digitalWrite(10, LOW);
digitalWrite(11, HIGH);
or
digitalWrite(11, LOW);
digitalWrite(10, HIGH);
There are two power systems. You can power two motors with a battery, but it may be drained quite quickly. This depends on how much current the motors use.
Connecting the + terminal of your battery to pin 8, and the - terminal to pins 4, 5, 12, 13
Connect the arduino +5V to pin 16, and Ground (Gnd) to pins 4,5, 12, 13.
Does that help?
GB