How to use L298N motor driver with battery
You should try to comply to the specification given in the  link you provided (see Electrical Characteristics below).

So, 


connect logic power supply to the +5V and GND on the left side of the board
Not connecting a supply (so, 'connecting 0V') conflicts with the lower limit of 4.5V.
increase the motor power supply (it should be higher than 7V).
It now is about 6V, which conflicts with the minimal required 7V.