Thanks for the schematic, that appears to be in order I can't see why it should give you trouble. However, I can't see what is powering the Nano on the schematic it looks like from the photograph this was when you were using the potential divider. This could be a problem because solderless bread board is notorious for having intermittent connections. It only takes the bottom leg to come out and you are applying 12V to the Nano.
This is bad because the heat sink for the regulator on the nano is just a small area of copper and it will quickly over heat.
The thinking is right but the implementation wrong.
Does that mean the resistors burned out? If so I am not surprised, if I read the colours correctly from the photograph, they are 10R and 22R, producing a current of 344mA down the chain and they look like only quarter watt resistors. Quite simply a potential divider is the wrong thing to do.
What I would be inclined to do is to fit a fixed 5V linear regulator to the motor voltage and feed that into the 5V pin of the nano. Don't forget the decoupling capacitors on the input and output of the board and maybe a heat sink on the regulator. Remember it is driving the HC-06 as well as the Nano.
I would also build this on strip board soldered up. However, those motor currents are too high even for strip board so I would also reinforce the current carrying capacity of the strips carrying current to and from the motor and driver with a length of tinned copper wire soldered over the track to finish off. You shouldn't be running a circuit like this on solderless bread board for long periods, it is only a very temporary soloution.
That is for each coil so a single motor will draw on avrage 2.6 Amps. As this is a chopping regulator then the peak current will be higher. Can your supply handle this?