Hi,
The correct way to do this:
* open the relay datasheet and look for the min pickup voltage
(This is the voltage where you can be sure the relay gets activated)
* find the according relay current
Now open the power supply datasheet
* and find the minimum expectable output voltage
Now open the L293D datasheet
* and find the expectable output voltage @ minimum supply voltage and min relay pickup current
If this output voltage is higher than the relay pickup voltage, then you are safe.
(Ignoring all wire resistance and other voltage drops)
Klaus