Be careful when wiring your Arduino and other hardware.
Check and doublecheck before you're powering up any part of it.
You've drawn a connection between Arduino pin 9 and VCC1 of the L293D, a power supply pin.
Arduino pin 9 should go to IC pin 9 i guess.
The L293D can handle 600 mA with a peak of 1.2 A.
What does your motor need ?
The inverters seem to be meant to prevent having both inputs (and outputs) at the same level and will save you an extra control pin on your Arduino.
This can make sense with steppers but i doubt it will make sense with a standard dc motor as you've drawn.
The way you've drawn your second sketch, Arduino pin 12 starts the motor, and pin 11 controls the direction it will run in.
Having IC pins 2 and 7 at the same level (either high or low), shorts the outputs and will brake the motor.
But that is impossible when using the inverters as drawn here.
So i wouldn't use them and use Arduino pins 12, 11 and 10 on IC pins 1, 2 and 7.
All connections you've drawn on the upper side of the breadboard are unused, as they go nowhere.
Be aware of heat that will need to be handled.
Having your setup on a breadboard isn't very good to ge rid of the heat.
You can find these things out yourself by studying the datasheet, which is exactly what i just did.